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Estimating biological reference points for Largehead hairtail (Trichiurus lepturus) fishery in the Yellow Sea and Bohai Sea
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Yupeng Ji1, Qun Liu1, *, Baochao Liao2, Qingqing Zhang1, Ya’nan Han1
Acta Oceanologica Sinica | 2019, 38(10) : 20 - 26
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Acta Oceanologica Sinica | 2019, 38(10): 20-26
• Marine Biology •
Estimating biological reference points for Largehead hairtail (Trichiurus lepturus) fishery in the Yellow Sea and Bohai Sea
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Yupeng Ji1, Qun Liu1, *, Baochao Liao2, Qingqing Zhang1, Ya’nan Han1
Affiliations
  • 1 Fisheries College, Ocean University of China, Qingdao 266003, China
  • 2 Department of Mathematics, Shandong University, Weihai 264209, China
Published: 2019-10-25 doi: 10.1007/s13131-019-1343-4
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It is important to find a reliable method to estimate maximum sustainable yield (MSY) or total allowable catch (TAC) for fishery management, especially when the data availability is limited which is a case in China. A recently developed method (CMSY) is a data-poor method, which requires only catch data, resilience and exploitation history at the first and final years of the catch data. CMSY was used in this study to estimate the biological reference points for Largehead hairtail (Trichiurus lepturus, Temminck and Schlegel) in the Yellow Sea and Bohai Sea, based on the fishery data from China Fishery Statistical Year Books during 1986 to 2012. Additionally, Bayesian state-space Schaefer surplus production model (BSM) and the classical surplus production models (Schaefer and Fox) performed by software CEDA and ASPIC, were also projected in this study to compare with the performance of CMSY. The estimated MSYs from all models are about 19.7×104–27.0×104 t, while CMSY and BSM yielded more reasonable population parameter estimates (the intrinsic population growth rate and the carrying capacity). The biological reference points of B/BMSY smaller than 1.0, while F/FMSY higher than 1.0 revealed an over-exploitation of the fishery, indicating that more conservative management strategies are required for Largehead hairtail fishery.

CMSY  /  surplus production models  /  maximum sustainable yield  /  Yellow Sea and Bohai Sea  /  Trichiurus lepturus
Yupeng Ji, Qun Liu, Baochao Liao, Qingqing Zhang, Ya’nan Han. Estimating biological reference points for Largehead hairtail (Trichiurus lepturus) fishery in the Yellow Sea and Bohai Sea[J]. Acta Oceanologica Sinica, 2019 , 38 (10) : 20 -26 . DOI: 10.1007/s13131-019-1343-4
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1 Introduction
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In China, fishery management methods are mainly the closure of summer season (May, June, July and August) and spawning ground, minimum mesh size regulation, and fishing power control (Wang, 2012; Shen and Heino, 2014; Yue et al., 2015). Because of the limited and poor data, maximum sustainable yield (MSY) in China fisheries are commonly unavailable, which may be one of the reasons that TAC (Total Allowable Catch) cannot be implemented in China (Wang, 2012). Therefore, it is important to find an appropriate method to estimate MSY or TAC for the fishery management in China.
Hairtail (Trichiurus lepturus) is widely distributed in the Yellow Sea and Bohai Sea. From 1986 to 2012 the total catches in the region for this fish species ranged from 7.38×104 to 32.89×104 t. Studies on this fish species have mostly concentrated on the effect of the Summer Fishing Moratorium Policy (Yan et al., 2007), the ecology (Wang, 2010), characteristics of reproduction and recruitment (Ling et al., 2005), the spawner-recruit model (Xu et al., 2011), the yield per recruit model (Ling et al., 2008) and surplus production models (Wang and Liu, 2013). The use of data-poor stock assessment models to analyze this fishery is not reported.
Surplus production models are among the simplest for a full fish stock assessment. Early versions of the surplus production model required equilibrium assumption, which is difficult to satisfy in practice, but it is not required by the modern production models. When the data lack contrast it means that the catch and effort data explain only a limited range of stock abundance levels. If the catch and effort data are representative for a fished stock, surplus production models may produce answers just as useful and sometimes better than those by age-structured models, at a lower cost (Haddon, 2011).
For the data-poor fisheries, some catch-based methods have been developed for estimating MSY, such as depletion-corrected average catch (DCAC) method (MacCall, 2009), stock reduction analysis (SRA, Kimura et al., 1984), and depletion-based stock reduction analysis (DB-SRA, Dick and MacCall, 2011). Martell and Froese (2013) and Froese et al. (2017) developed a Catch–MSY model (CMSY) based on catch data, resilience information, and assumptions about relative biomass of the first and last years. In comparison with the other data poor methods, an FAO workshop (Rosenberg et al., 2014) concluded that CMSY performed the best, although the other models performed similarly in many cases. CMSY was better in estimating status over short time scales and could be particularly useful in developing countries where data time series are usually short. Harvest dynamics was an important explanatory variable, which indicate the importance of having accurate data on catch and fishing effort.
Therefore, CMSY method is used in this study for stock assessment of Largehead hairtail Trichiurus lepturus (Temminck and Schlegel) fishery in the Yellow Sea and Bohai Sea. This study could be useful for determining MSY on data-limited fisheries in China. The results of CMSY are also compared with those from surplus production models, including the classical forms (Schaefer and Fox) performed by software CEDA and ASPIC, and extensions, Bayesian state-space Schaefer surplus production model. Wang and Liu (2013) and Zhang et al. (2018a, b) estimated MSY of largehead hairtail fishery in the East China Sea using surplus production models and CMSY methods, but little work has been done on the biological reference points of the species in the Yellow Sea and Bohai Sea, especially using the data-poor method of CMSY.
2 Materials and methods
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2.1 Data sources
Fishery statistics of Largehead hairtail T. lepturus fishery in the Yellow Sea and Bohai Sea of the 27 years (1986–2012) were collected from China Fishery Statistical Year Books (Fishery Bureau of Agriculture Ministry, China, 1986–2012), catch per unit effort (CPUE) is calculated from the catch and effort data. Catch data are in tons and CPUEs are in t/KW in each year (Table 1).
2.2 CMSY model
On the basis of catch data, resilience or productivity of the fish species and stock status at the beginning and the end of the time series, CMSY is a Monte-Carlo method that estimates fisheries reference point of MSY (Martell and Froese, 2013; Froese et al., 2017).
The fish population dynamics are based on the Schaefer surplus production model (Schaefer, 1991):
${B_t} = {\lambda _0}k{{\rm e}^{{v_t}}}\;\;{\rm{when}}\;\;t = 1,$
${B_t} = \left[ {{B_{t - 1}} + r{B_{t - 1}}\left( {1 - \frac{{{B_{t - 1}}}}{k}} \right) - {C_{t - 1}}} \right] \times {{\rm e}^{{v_{t - 1}}}}\;\;{\rm{when}}\;\;t > 1,$
where B is biomass, C is catch, r is the intrinsic population growth rate, k is the carrying capacity, t is year, and νt is a normal error with mean 0 and variance σ2. λ0 is the initial depletion level (B1/k).
For r–k combinations, if the population exceeding k or going extinct, 0 was assigned, and if the final depletion level is between the final depletion levels λ1 and λ2, 1 was assigned. Therefore, the likelihood function of Θ ={r, k} can be expressed as
$\begin{array}{l}L(\varTheta |{C_t}) = \left\{\begin{array}{l}1\;\;\;\;\;{\lambda _1} \leqslant {B_{n + 1}}/k \leqslant {\lambda _2},\\0\;\;\;\;\;{\lambda _1} > {B_{n + 1}}/k > {\lambda _2},\end{array}\right.\end{array}$
where n is the number of years in the data series, t=1, 2, …, n. Therefore, for each pair of parameter combination (r, k) that produces a viable population at the end of the catch data, MSY can be calculated from MSY=r×k/4.
CMSY requires prior information for r and k parameters. The lower and upper boundaries of k are the maximum catch in the data series and 50 times maximum catch respectively. In this study for Largehead hairtail T. lepturus fishery in the Yellow Sea and Bohai Sea the prior range for k is calculated by the R-code of Froese et al. (2017). According to prior ranges for parameter r based on classification of resilience (see below) in the user guide of Froese et al. (2017), we used r range of 0.2–0.8 for medium resilience:
Exploitation history at the first and final years is from the catch data. Prior initial relative biomass is 0.1–0.4, prior final relative biomass is 0.2–0.65. Prior intermediate relative biomass is 0.5–0.9 in year 2005 by default. More details of CMSY are in Martell and Froese (2013) and Froese et al. (2017).
2.3 Surplus production models
Compared to other implementations of surplus production models, Bayesian state-space Schaefer surplus production model (BSM) has the focus on informative priors and the acceptance of fragmented abundance data (Millar and Meyer, 1999; Froese et al., 2017). Prior range for r and k are the same as those in CMSY. The prior range of q is calculated by the R-code of Froese et al. (2017).
Classical surplus production models (SPM) are also included in this paper for the purpose of comparison. The most commonly used model is Schaefer model, which is built on the logistic population growth model (Schaefer, 1991):
$\frac{{{\rm{d}}B}}{{{\rm{d}}t}} = rB\left( {k - B} \right).$
Next Fox (1970) proposed further work on a Gompertz growth equation:
$\frac{{{\rm{d}}B}}{{{\rm{d}}t}} = rB\left( {{\rm{ln}}k - {\rm{ln}}B} \right).$
Both the two classical SPMs (Schaefer and Fox) are performed by computer software packages, CEDA (a catch effort data analysis, Hoggarth et al., 2006) and ASPIC (a surplus production model incorporating covariates, Prager, 2017). Because ASPIC does not provide the estimates of r and k, we calculated r from 2×FMSY, and k from 2×BMSY for Schaefer SPM and BMSY/0.679 for Fox SPM.
We used an R-code (CMSY_O_7q.R) from Froese et al. (2017) (downloaded from http://oceanrep.geomar.de/33076/) for CMSY and BSM. The input values for the CMSY/BSM program are in Table 2. The input values of ASPIC are in Appendix. CEDA is menu driven, it requires catch/effort data and an initial proportion (calculated as the ratio of start catch over maximum catch).
3 Results
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The population parameters (r and k) and biological reference point (MSY) were estimated by these six methods for Largehead hairtail (T. lepturus) in the Yellow Sea and Bohai Sea (Table 3). All the methods estimated similar MSY values (in a range of 19.7×104–27.0×104 t). The parameter estimates (r and k) from CMSY and BSM were much close. However, the traditional surplus production models calculated small population growth rates (0.055–0.14) while with high carrying capacity estimates (781×104–1 372×104 t). The confidence interval of r, k and MSY estimated from the traditional surplus production models were much wider than those from CMSY and BSM. In contrast the new methods of CMSY and BSM produced reasonable values of both the above parameters.
Based on the parameters and MSY estimates, BSM provided the information for management for Largehead hairtail (T. lepturus) in the Yellow Sea and Bohai Sea (Fig. 1). B/BMSY and F/FMSY from the models are in Table 4. Except for the CMSY results, the values of B/BMSY and F/FMSY from all the other models showed that the biological reference points of B/BMSY were mostly smaller than 1.0, while F/FMSY were mostly higher than 1.0, indicating the overfishing and overfished status of this fishery.
4 Discussion
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4.1 CMSY model
The prior information of r and k parameters is needed for methods of CMSY and BSM. Martell and Froese (2013) suggested that the prior of r could be acquired from the resilience in FishBase (Froese and Pauly, 2018). Apart from that, r may be estimated from an empirical equation (Sullivan, 1991) based on von Bertalanffy growth parameters of the exponential growth rate, K, and the asymptotic weight, W∞. The estimations of K and W∞ could be obtained using the ELEFAN method in FiSAT computer software package (Gayanilo et al., 2005). The predictive equation (Sullivan, 1991) is
$r = 0.947 + 1.189K - 0.095\ln ({W_\infty }).$
The above equation suggests that faster growth and smaller body size can have a high intrinsic rate of increase. Moreover, r prior values may be related to natural mortality M (r=2M) (Froese et al., 2017). The M estimates may be obtained from an empirical formula of Pauly (1980) and the natural mortality estimators for information-limited fisheries are reviewed by Kenchington (2015).
Simulation tests (ICES, 2015) suggest that CMSY analysis may be less well suited for lightly exploited stocks and/or for species with very low resilience. The Largehead hairtail (T. lepturus) fishery in the Yellow Sea and Bohai Sea does not fit in these two categories (Wang and Liu, 2013; Zhang et al., 2018b), so the CMSY method can provide a good fit. Therefore this model may present a useful alternative approach for the fish stock assessment in China. However in the situation where the ecological strategy of fish has changed, r estimation must be carefully considered.
The results showed that r estimates from the surplus production models of CEDA and ASPIC are lower than expected. Because a given time series of catches could be explained by a large stock size with low productivity or by a small stock size with high productivity, the estimated fish population parameters of r and k should be cautiously considered even if the estimated MSY is reasonable. The mechanisms and algorithms of CMSY and ASPIC are different in estimating parameters but should give equivalent or similar answers unless r and k are not fully estimable given the data used. In this case, it can be diagnosed by plotting the likelihood profile or looking at the posterior MCMC (Jiao Yan, personal communication). We hope to investigate this for the Largehead hairtail fishery data in our future work.
4.2 Surplus production models
Surplus production models are among the classic fish stock assessment models which require catch and effort/CPUE data. Even though the concept of MSY had been criticized in the history of fishery science, it remains still an important biological reference point (ICES, 2015). Recent advances of mathematics and computer science enabled extensions of surplus production models, such as BSM, which can consider the priori and posteriori fish population parameters (Froese et al., 2017).
4.3 Largehead hairtail (T. lepturus) fishery
The Largehead hairtail (T. lepturus) is one of the most important fisheries in China. In the Yellow Sea and Bohai Sea the fishery started in 1960s, whose catch peaked at 328 927 t in 2006 and then declined to 167 319 t in 2012 (Table 1). Recently the age composition of the catch is largely 1 year, and there are clear evidences of early maturation, prolonged spawning season and increased young fish. Even though these biological characteristics can compensate the effects from heavy fishing, but they are not limitless. There are signs that the over-exploitation has exceeded the carrying capacity of the species, the fishery is still in declining. Apart from the effects of over-exploitation from excess fishing effort, the climate change may also affect the fish population dynamics of this species①.
In the past decades the mean anal length and mean anal length at maturity of Largehead hairtail had decreased, while the growth coefficient and exploitation rate of Largehead hairtail had increased (Table 5). This indicates that the ecological strategy of this fish has changed. Therefore the application of CMSY method (as well as any other fish stock assessment models) should be carefully considered.
In conclusions, the population of Largehead hairtail in the Yellow Sea and Bohai Sea was overfished and overfishing, indicating that more conservative management strategy is required for the fishery of this important species. The biological reference points estimated in this study could provide scientific background for the management of the Largehead hairtail fishery. Compared with the classical surplus production models performed by software CEDA and ASPIC, CMSY and BSM provided more reasonable estimates for the population parameters and biological reference points for the Largehead hairtail, which can be applied to the stock assessment and fishery management of many other fishery species, especially for those species with limited data in China.
Acknowledgements
We thank Yan Jiao and Qiuyun Ma for their comments to improve this manuscript.
Funding
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  • The National Natural Science Foundation of China under contract No. 31772852.
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Article Info
doi: 10.1007/s13131-019-1343-4
  • Receive Date：2018-07-03
  • Online Date：2026-04-01
  • Published：2019-10-25
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History
  • Received：2018-07-03
  • Accepted：2018-10-15
Funding
The National Natural Science Foundation of China under contract No. 31772852.
Affiliations
    1 Fisheries College, Ocean University of China, Qingdao 266003, China
    2 Department of Mathematics, Shandong University, Weihai 264209, China

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表12种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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