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Estimating blue marlin (Makaira nigricans) sustainable yield in the Indian Ocean using a data-poor approach
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Estimating blue marlin (Makaira nigricans) sustainable yield in the Indian Ocean using a data-poor approach Yuwei Fana,b, Zhe Genga,b, Jiangfeng Zhua,b, Xiaojie Daia,b,∗, Kindong Richardc,d a
College of Marine Sciences, Shanghai Ocean University, Shanghai, 201306, China Key Laboratory of Oceanic Fisheries Exploration, Shanghai Ocean University, Ministry of Agriculture, Shanghai, 201306, China c National Engineering Research Center for Oceanic Fisheries, Shanghai, 201306, China d Scientific Observing and Experimental Station of Oceanic Fisheries Resources and Environment, Ministry of Agriculture, Shanghai, 201306, China b
ARTICLE INFO
ABSTRACT
Keywords: Blue marlin Data-poor approach Stock assessment Indian Ocean
Blue marlin (Makaira nigricans) is a common bycatch species in the global tuna longline fishery. In this study, we applied a common data-poor approach, i.e., depletion-corrected average catch (DCAC) to assess stock status of the Indian Ocean blue marlin. Sustainable yield (Ysust), one reference point in this case, was estimated, and its uncertainty was integrated by using Monte Carlo simulation. The results revealed the estimate of Ysust by DCAC was lower than MSY of 11,926 t by BSP-SS and is also lower than the provisional reference point of 11,704 t by the management proposal. DCAC is reliable for blue marlin in driving precautionary management quantity based on the CPUE of Japan (1980–2015). This study also implies that DCAC could be applied to other billfish stocks and uncertainty be estimated for sustainable yield. However, data-poor methods could be adjusted with precautionary approaches.
1. Introduction Billfishes, excluding swordfish, are typically not the primary targets of large-scale fisheries, which have historically led to a lack of targeted monitoring efforts (Punt, Su, & Sun, 2015). This is also true for the tuna fisheries in the Indian Ocean where the majority of billfishes are taken as bycatch (IOTC-WPB14, 2016). Estimates of catch for billfishes are likely less reliable than those for tunas because a greater fraction of the catch is taken in recreational fisheries or as bycatch which tend to be less well sampled than commercial fisheries (Punt et al., 2015). This poses a significant challenge for the assessment and management of billfishes. For example, the sailfish and shortbill spearfish in the Indian Ocean are seldom the primary focus for data collection efforts and it is difficult to assess them using conventional stock assessment models. Thus, the Indian Ocean Tuna Commission (IOTC) recommended that data-poor approaches be applied to billfish species (e.g. sailfish) in the Indian Ocean (IOTC-WPB14, 2016). Data-poor approaches have attracted worldwide attentions in the recent years. In 2006, The United States Congress introduced annual catch limits (ACLs) to limit catch and trigger measures to ensure accountability (Newman, Berkson, & Suatoni, 2015). Subsequently, more than 16 methods were adopted in establishing catch limits for datalimited fisheries (Newman et al., 2015). “Data-poor Approach for
∗
Fishery” was listed as one of the four themes by World Stock Assessment Method Conference in 2013 (Cadrin & Dickey-Collas, 2015). The ideal approach to apply a new data poor method is to evaluate its robustness to various assumptions by simulation testing (Arnold & Heppell, 2015). However, simulation testing is time consuming and in practice many stock assessments are being directly conducted without simulation testing for the assessment method, and key uncertainties are addressed by running plausible sensitivity analyses (Deroba et al., 2015). Applying a data poor method to a stock without any testing might be risky when management advices are to be developed. For example, the data poor method was recommended for Indian Ocean sailfish (IOTC-WPB14, 2016), however, there was lack of capacity and resources to conduct simulation testing within the Working Party on Billfish (WPB). One possible solution to this is to apply data poor methods that have been approved to be reliable for another stock with similar biology and fishery history. The Indian Ocean blue marlin (Makaira nigricans) seemed a possible stock to satisfy this exercise. Data-poor methods include those that set acceptable biological catch (e.g., Depletion-Based Stock Reduction Analysis or DB-SRA; Dick & MacCall, 2011) and those that estimate sustainable yield (e.g., Depletion-Corrected Average Catch or DCAC; MacCall, 2009). DCAC is a common catch-based method stemming from the work of Restrepo et al. (1998) and relies on catch data to estimate sustainable yield. The
Corresponding author. College of Marine Sciences, Shanghai Ocean University, Shanghai, 201306, China. E-mail address: [email protected] (X. Dai).
https://doi.org/10.1016/j.aaf.2019.02.001 Received 19 September 2018; Received in revised form 13 January 2019; Accepted 1 February 2019 2468-550X/ © 2019 Published by Elsevier B.V. on behalf of Shanghai Ocean University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
Please cite this article as: Yuwei Fan, et al., Aquaculture and Fisheries, https://doi.org/10.1016/j.aaf.2019.02.001
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uncertainty of estimates with respect to key model parameters can be quantified by running Monte Carlo simulation. This method was mainly applied to some American fisheries, such as fisheries managed by the South Atlantic Fishery Management Council and the Mid-Atlantic Fishery Management Council (Carruthers et al., 2014). This method has also been used for the U.S. west coast groundfish (Wetzel & Punt, 2015). Billfishes (the collective name for marlins, sailfishes, and shortbill Spearfishes) are large, swiftly swimming, epipelagic, apex ocean predators (Habegger, 2014). Their morphological taxonomy was reviewed by Nakamura (1985) and a new genetics-based taxonomy given by Collette, Mcdowell, and Graves (2006). They are surface dwellers and distribute in shallower water (near-shore) (Young et al., 2011). During the summer, they move into productive warm-temperate waters for heavy feeding, and in autumn, they move back to tropical waters for overwintering and spawning (Chiang et al., 2006). In Indian Ocean, blue marlin is a billfish species with medium fishery data. The blue marlin occurs throughout tropical and subtropical waters of the Pacific, Atlantic and Indian Ocean (Nakamura, 1985). They are a bycatch species that require catch-effort statistics for stock assessments (Goodyear & Phillip, 2016). The Indian Ocean blue marlin was successfully assessed by IOTC WPB using state-space Bayesian production model (BSP-SS; IOTC-WPB14, 2016) and management advice was developed. Thus, our intention is to choose a candidate data poor method to Indian Ocean blue marlin and evaluate its reliability in developing management quantity. In this study, we applied the DCAC to Indian Ocean blue marlin to estimate sustainable yield (Ysust) and compared it with maximum sustainable yield (MSY) estimated by the state-space Bayesian production model. Stock assessment methods relying on different data and assumptions often lead to differences in estimates of management quantities. However, if the estimate of Ysust by DCAC is lower than MSY by BSP-SS, the Ysust can be regarded as precautionary management quantity and it suggests that the DCAC be a reliable data poor method in developing Ysust based management advice.
Fig. 1. Combined blue marlin catches in the IOTC database (1950–2015).
2001; Pine et al., 2008). The natural mortality was thus calculated to be 0.41 year−1. 2.3. Estimation methods 2.3.1. Basic equation of DCAC Normally, DCAC relied on the annual catch data, the relative decline in abundance (Δ), the natural mortality, and the ratio of FMSY (fishing mortality rate corresponding to MSY) to M (MacCall, 2009). Δ could be calculated by the relative reduction from the first year (FYR) to the last year (LYR) of the catch time series and its computation formula is as follows:
=
B MSY B0
n+
(
FMSY M
)M
1
(3)
Where ∑C is total catches, n is the length of the time series, B0 is virgin biomass, BMSY is biomass which produces MSY and BMSY/B0 is the biomass of the maximum Ysust relative to the carrying capacity. Restrepo et al. (1998) proposed the ratio of FMSY to M (c), so the Ysust is
Blue marlin is a bycatch species of tuna longline and gillnets fleets operating in the Indian Ocean and it is largely seen as a non-target species of industrial and artisanal fisheries. The main data required for DCAC method is total catch. In recent years, the fleet of Taiwan, China (longline) accounted for around 33% of total catches of blue marlin; and the fleet of Indonesia (fresh longline) and Pakistan (gillnet) accounted for around 28% and 14% of total catches, respectively (IOTCWPB14, 2016). Longline catches account for around 74% of total catches, followed by gillnets (23%), with remaining catches recorded under troll and handline fisheries (IOTC-WPB14, 2016). In this study, the combined catch data and two CPUE indexes from Japan and Taiwan, China of the blue marlin to be used by DCAC was downloaded from IOTC website (www.iotc.org) and time series of catch is 1950–2015 (Fig. 1).
Ysust =
C n+
(
B MSY cM B0
)
1
(4)
Input information includes the sum of catches and associated number of years, the relative reduction in biomass during that period, M, and the assumed ratio of FMSY to M (MacCall, 2009). With all these being set, the assessment with uncertainty was integrated by Monte Carlo simulation, and a random re-sampling was done 10,000 times in order to generate the probability distribution of Ysust. 2.3.2. Parameter setting Due to lack of accurate fishery data, Δ was unable to be precisely estimated. There is no clear value of Δ that can serve as a default and if nothing at all is known about the value of Δ, it may be appropriate to assume three parameters of different levels, 0.3, 0.5, 0.7 for precautionary purpose. Most fishery stock–recruitment relationships indicated that BMSY < 0.5B0, and according to various previous researches (Clark, 1991; NMFS, 1998; Restrepo et al., 1998), for most teleosts including blue marlin the ratio of BMSY to B0 is approximately 0.4. In this study, two levels of density dependence (0.4 and 0.6) were assumed for BMSY/B0. In some fishery cases with limited data, Thompson (1993) and NMFS (1996) suggested the assumption of c = 0.8 and c = 0.75.
2.2. Estimation of natural mortality Natural mortality rate (M) was obtained by the Pauly (1980)'s formula with growth parameter k, gradual length L (cm) and annual average surface temperature T, as shown below:
0.279 ln L + 0.6543 ln k + 0.463 ln T
(2)
C
Ysust =
2.1. Data resources
0.0152
BLYR B0
The DCAC provides an estimate of the yield (Ysust) that would keep the stock sustained:
2. Material and methods
ln M =
BFYR
(1)
Where L was 244 cm, and it was based on fitting von Bertalanffy growth curve to the size-at-age data of Prince, Lee, Zweifel, and Brothers (1991) and Wilson (1984). The growth parameters (k) was 0.28 year−1 which was obtained using Pine, Martell, Jensen, Walters, and Kitchell (2008). The SST was 26 °C as used in other study (Hinton, 2
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3. Results
Table 1 Specification of DCAC for Indian Ocean blue marlin. Δ
Bmsy/B0 = 0.4 c
0.3 0.5 0.7
3.1. Estimation of sustainable yield based on different parameter assumptions
Bmsy/B0 = 0.6
0.6
0.8
1.0
0.6
0.8
1.0
A1 B1 C1
A2 B2 C2
A3 B3 C3
A4 B4 C4
A5 B5 C5
A6 B6 C6
The probability distribution of Ysust is shown in Fig. 2. The maximum median of the estimate of Ysust is 6800 t and the minimum median is 6190 t. The estimation varied as low as 10% and the parameters had little influence on the estimate of Ysust in accordance with results from Fig. 3. The estimates for sustainable yield were not sensitive to the choices of Δ or c and the estimate of Ysust is about 6000 t to 7000 t (Fig. 3). The estimate of Ysust decreased lightly with the increase of depletion level (Δ), and increased lightly with the ratio of FMSY to M (Fig. 3). The sensitivity analysis to M showed that, M = 0.2 resulted in a lower estimate of Ysust and decreased over M = 0.41 by 5.05% (Fig. 4). The estimate of Ysust increased with the increase of M (Fig. 4). Ysust based on different parameter assumptions was lower than the MSY of 11,926 t by BSP-SS and the DCAC method appeared relatively robust to the different parameters.
Table 2 Specification of Δ based on CPUE data. Fleet of longline CPUE
Time window
Reduction in biomass (Δ)
Japan Japan Japan Japan Taiwan, China Taiwan, China Taiwan, China
1971–2015 1980–2015 1990–2015 2000–2015 1980–2015 1990–2015 2000–2015
0.45 0.58 0.06 0.07 −0.20 −0.53 −0.22
3.2. The influence of catch time series on the estimation of sustainable yield According to the catch data of the blue marlin in the Indian Ocean (1950–2015) (Fig. 1), the Ysust was estimated using different catch time series and a clearly increasing trend was observed depending on the data set. The minimum median of the estimate of Ysust is 6610 t when the 1950–2015 catch time series was selected. The median of the estimate of Ysust of about 9700 t is close to the MSY of 11,926 t by BSP-SS when catch time series for 1990–2015 and 2000–2015 were used (Fig. 5).
For Indian Ocean blue marlin, three different levels of c were assumed and a total of 18 models were considered (3 × 2 × 3 = 18). DCAC analysis was developed as shown in Table 1. MacCall (2009) suggested that in terms of natural mortality rate (M), the use of DCAC is not recommended if M is greater than ∼0.2 year−1, above which the depletion correction becomes small. In this paper, the M = 0.41 year−1 based on Equation (1), we also set a level of M = 0.2 year−1 to evaluate the sensitivity of estimates of Ysust to M. Ysust was estimated based on standardized CPUE time series from Japanese longline fishery (1971–2015) and Taiwanese longline fishery (1980–2015), respectively. We tested different sets of the same time series by decade and the assumed Δ is listed in Table 2. The time series block by decade was chosen subjectively.
3.3. Estimation of sustainable yield based on different CPUE series The probability distribution of blue marlin Ysust shown in Fig. 6 is based on two different CPUE indexes. There were some differences in the results based on the different CPUE time series and the estimate of Ysust increased when time series data was shortened. The minimum median of the estimate of Ysust was 7550 t based on the CPUE series of
Fig. 2. Frequency distribution of sustainable yield for blue marlin with Monte Carlo simulations. 3
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Fig. 3. Estimation of sustainable yield of Indian Ocean blue marlin using DCAC. Dashed lines stand for the average catch (1950–2015).
4. Discussion 4.1. Management implication of sustainable yield estimates Different assessment models rely on the same or different theories, hypotheses, types of data (including biological information, fisherydependent and -independent data) and statistical methods. Indian Ocean blue marlin was assessed by the state-space Bayesian production model in the Working Party of Billfish meeting in 2016 (IOTC-WPB14, 2016). The estimate of Ysust by DCAC was lower than MSY of 11,926 t by BSP-SS. This implied that the Ysust by DCAC could be regarded as precautionary management quantity and it suggests that the DCAC be a reliable data poor method in developing Ysust based management advice for Indian Ocean blue marlin. With data-rich methods (e.g., that estimate a stock-recruitment relationship) we can derive an estimate for MSY, however data-poor methods make a lot of assumptions and since we are not estimating any kind of stock recruitment relationship. We don't have the data to come up with an analytical “solution” for MSY so we are left with making an approximation with DCAC.
Fig. 4. Sensitivity analysis for the estimate of sustainable yield and natural mortality rate used in the DCAC model.
4.2. Implication of DCAC to other billfish species The majority of billfish stocks lack sufficient catch, survey, and other biological data to calculate current abundance and productivity using conventional stock assessment methods, requiring the use of alternative, data-limited methods (Carruthers et al., 2014). Other species such as Sailfish and Shortbill spearfish are considered as data-poor stocks (e.g. no reliable abundance index and size composition). Compared with other data sources, the data on catches can be considered as amongst the most reliable available for billfishes except when catches are known to be substantially underestimated (Hinton & Maunder, 2014). These billfishes are believed to be similar to blue marlin in terms of biology, fishery history and data pattern. Blue marlin was used to test whether the data-poor approach can be applied in billfishes. Result from this study suggested that DCAC can be used to estimate Ysust for Indian Ocean blue marlin, as shown by its conservative estimate of Ysust, compared with MSY by BSP-SS. If the reasonable time
Fig. 5. Sustainable yield of blue marlin estimated by DCAC based on different time series.
Japan (1971–2015) (Table 3). The median of the estimate of Ysust based on the CPUE series of Taiwan, China (1990–2015, 2000–2015) is over the MSY of 11,926 t by BSP-SS. 4
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Fig. 6. Distribution of sustainable yield estimated based on CPUEs from Taiwan, China, and Japan.
change in time series after catch increases. Common empirical methods for estimating M include formulas obtained by Pauly (1980), Hoenig (1983) and Jensen (1996) et al. Hinton (2001) calculates M values at 0.41 year−1 for males by Pauly (1980)'s method. In this paper, the natural mortality (M) is calculated as 0.41 year−1 by Pauly's method and it is almost similar to M = 0.38 year−1 (approx. 95% confidence interval 0.30–0.45 year−1) from the MULTIFAN-CL model in Kleiber, Hinton, and Uozumi (2003). The natural mortality used is quite a bit higher than that suggested by the MacCall (2009) paper and considering whether the depletion correction has an impact on the model, we compared the results of M = 0.2 and M = 0.41. The result shows the estimate of Ysust increased with the increase of M (Fig. 3) and variation trend of M is the same as that of parameter c, which is not sensitive to this model. The M = 0.4 resulting in a slightly higher estimate of Ysust compared with M = 0.2 by 5.05%, indicating that the influence of M on the result is minor for blue marlin even if we assumed a doubled value of M (Fig. 3). This study showed that DCAC could be used to estimate sustainable yield for the Indian Ocean blue marlin and consequently be used to give some management advice for this data-poor fishery. However, the results of this study should not be used directly to develop management advices, but use recent data and follow recommendations from the IOTC scientific commission before its practical applicability. In addition, its applicability remains to be further studied in the case of data mis-reporting and/or non-reporting.
Table 3 Sustainable yield of blue marlin estimated by DCAC based on different CPUEs. Data source
Time Series
Mean/1000t
Median/1000t
Japan Japan Japan Japan Taiwan, China Taiwan, China Taiwan, China
1971–2015 1980–2015 1990–2015 2000–2015 1980–2015 1990–2015 2000–2015
7.30 7.93 10.81 12.38 11.01 19.25 22.09
7.55 8.27 10.64 11.27 9.68 12.74 12.83
series and Δ was considered, DCAC is reliable for blue marlin in deriving precautionary management quantity, which can provide management advice in term of catch limit. Also, if the conventional stock assessments cannot be conducted, data-poor approaches such as the DCAC could be applied to other billfishes and their uncertainty be estimated for sustainable yield. 4.3. Sensitivity to assumptions In this study, the estimate of Ysust by DCAC was lower than the provisional reference point of 11,704 t by the management proposal. This suggested that the Ysust estimated by DCAC was more conservative. Ysust of about 6300 t by 18 DCAC analyses (1950–2015 catch time series) is not very sensitive to the parameters and appears relatively robust to the different parameters (Fig. 2). According to MacCall (2009) and Geng et al. (2017), Ysust will increase with c, and the probability distribution can gradually reach stable with the increase of c, which is consistent with the results of this study. The choice of time series has great influence on DCAC results. Considering the great changes in the catch data of the blue marlin in the Indian Ocean (1950–2015) (Fig. 1), we tested different catch time series. There were significant differences between the estimations of Ysust based on each of the five catch series. The estimate of Ysust increased gradually with the decrease of the time series and tended to reach stable after 1980. The estimates of Ysust were both about 9000 t for 1980–2015 and 1990–2015, which was closer to the MSY estimated by the BSP-SS. In terms of time series, we recommend the use of time series after 1980, with small sensitivity. The Δ values of Taiwanese fleets were negative and hence we simulated based on the standardized CPUE submitted by Japan longline fleets (1971–2015) and the standardized CPUE submitted by Taiwan, China longline fleets (1980–2015). Which the evaluation results of the Japanese group are the most optimistic, sustainable yield is evenly distributed. The relative reduction of Taiwanese group is negative (Δ ≤ −0.2), and susceptible to extreme value (1990–2015, 2000–2015), and short time series, reduces the DCAC model fault tolerance, which is easy to produce abnormal results (Geng et al., 2017). Based on the above analysis, the estimate of Ysust based on the CPUE of Japan (1980–2015) was reliable. Similarly, the best fit for time series would be the section where sudden
Acknowledgements This study was funded by National Natural Science Foundation of China (#41676120). The catch data sets analyzed in the study were originally from fishing fleets of IOTC, compiled by IOTC secretariat and further improved by the IOTC WPB. The longline CPUE indices were developed by scientists from Japan and Taiwan, China. Special thanks go to Kindong Richard for giving suggestions and revisions. Any discussion or conclusion in this study only reflects the views of authors. References Arnold, L. M., & Heppell, S. S. (2015). Testing the robustness of data-poor assessment methods to uncertainty in catch and biology: A retrospective approach. ICES Journal of Marine Science, 72(1), 243–250. Cadrin, S. X., & Dickey-Collas, M. (2015). Stock assessment methods for sustainable fisheries. ICES Journal of Marine Science, 72(1), 1–6. Carruthers, T. R., Punt, A. E., Walters, C. J., MacCall, A., Mcallister, M. K., Dick, E. J., et al. (2014). Evaluating methods for setting catch limits in data-limited fisheries. Fisheries Research, 153(5), 48–68. Chiang, W. C., Sun, C. L., Yeh, S. Z., Su, W. C., Liu, D. C., & Chen, W. Y. (2006). Sex ratios, size at sexual maturity, and spawning seasonality of sailfish istiophorus platypterus from eastern taiwan. Bulletin of Marine Science -Miami-, 79(3), 727–737. Clark, W. G. (1991). Groundfish exploitation rates based on life history parameters. Canadian Journal of Fisheries and Aquatic Sciences, 48(5), 734–750. Collette, B. B., Mcdowell, J. R., & Graves, J. E. (2006). Phylogeny of recent billfishes (xiphioidei). Bulletin of Marine Science, 79(79), 455–468. Deroba, J. J., Butterworth, D. S., Methot, R. D., Oliveira, J. A. A. D., Fernandez, C., Nielsen, A., et al. (2015). Simulation testing the robustness of stock assessment
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Estimating blue marlin (Makaira nigricans) sustainable yield in the Indian Ocean using a data-poor approach Yuwei Fana,b, Zhe Genga,b, Jiangfeng Zhua,b, Xiaojie Daia,b,∗, Kindong Richardc,d a
College of Marine Sciences, Shanghai Ocean University, Shanghai, 201306, China Key Laboratory of Oceanic Fisheries Exploration, Shanghai Ocean University, Ministry of Agriculture, Shanghai, 201306, China c National Engineering Research Center for Oceanic Fisheries, Shanghai, 201306, China d Scientific Observing and Experimental Station of Oceanic Fisheries Resources and Environment, Ministry of Agriculture, Shanghai, 201306, China b
ARTICLE INFO
ABSTRACT
Keywords: Blue marlin Data-poor approach Stock assessment Indian Ocean
Blue marlin (Makaira nigricans) is a common bycatch species in the global tuna longline fishery. In this study, we applied a common data-poor approach, i.e., depletion-corrected average catch (DCAC) to assess stock status of the Indian Ocean blue marlin. Sustainable yield (Ysust), one reference point in this case, was estimated, and its uncertainty was integrated by using Monte Carlo simulation. The results revealed the estimate of Ysust by DCAC was lower than MSY of 11,926 t by BSP-SS and is also lower than the provisional reference point of 11,704 t by the management proposal. DCAC is reliable for blue marlin in driving precautionary management quantity based on the CPUE of Japan (1980–2015). This study also implies that DCAC could be applied to other billfish stocks and uncertainty be estimated for sustainable yield. However, data-poor methods could be adjusted with precautionary approaches.
1. Introduction Billfishes, excluding swordfish, are typically not the primary targets of large-scale fisheries, which have historically led to a lack of targeted monitoring efforts (Punt, Su, & Sun, 2015). This is also true for the tuna fisheries in the Indian Ocean where the majority of billfishes are taken as bycatch (IOTC-WPB14, 2016). Estimates of catch for billfishes are likely less reliable than those for tunas because a greater fraction of the catch is taken in recreational fisheries or as bycatch which tend to be less well sampled than commercial fisheries (Punt et al., 2015). This poses a significant challenge for the assessment and management of billfishes. For example, the sailfish and shortbill spearfish in the Indian Ocean are seldom the primary focus for data collection efforts and it is difficult to assess them using conventional stock assessment models. Thus, the Indian Ocean Tuna Commission (IOTC) recommended that data-poor approaches be applied to billfish species (e.g. sailfish) in the Indian Ocean (IOTC-WPB14, 2016). Data-poor approaches have attracted worldwide attentions in the recent years. In 2006, The United States Congress introduced annual catch limits (ACLs) to limit catch and trigger measures to ensure accountability (Newman, Berkson, & Suatoni, 2015). Subsequently, more than 16 methods were adopted in establishing catch limits for datalimited fisheries (Newman et al., 2015). “Data-poor Approach for
∗
Fishery” was listed as one of the four themes by World Stock Assessment Method Conference in 2013 (Cadrin & Dickey-Collas, 2015). The ideal approach to apply a new data poor method is to evaluate its robustness to various assumptions by simulation testing (Arnold & Heppell, 2015). However, simulation testing is time consuming and in practice many stock assessments are being directly conducted without simulation testing for the assessment method, and key uncertainties are addressed by running plausible sensitivity analyses (Deroba et al., 2015). Applying a data poor method to a stock without any testing might be risky when management advices are to be developed. For example, the data poor method was recommended for Indian Ocean sailfish (IOTC-WPB14, 2016), however, there was lack of capacity and resources to conduct simulation testing within the Working Party on Billfish (WPB). One possible solution to this is to apply data poor methods that have been approved to be reliable for another stock with similar biology and fishery history. The Indian Ocean blue marlin (Makaira nigricans) seemed a possible stock to satisfy this exercise. Data-poor methods include those that set acceptable biological catch (e.g., Depletion-Based Stock Reduction Analysis or DB-SRA; Dick & MacCall, 2011) and those that estimate sustainable yield (e.g., Depletion-Corrected Average Catch or DCAC; MacCall, 2009). DCAC is a common catch-based method stemming from the work of Restrepo et al. (1998) and relies on catch data to estimate sustainable yield. The
Corresponding author. College of Marine Sciences, Shanghai Ocean University, Shanghai, 201306, China. E-mail address: [email protected] (X. Dai).
https://doi.org/10.1016/j.aaf.2019.02.001 Received 19 September 2018; Received in revised form 13 January 2019; Accepted 1 February 2019 2468-550X/ © 2019 Published by Elsevier B.V. on behalf of Shanghai Ocean University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
Please cite this article as: Yuwei Fan, et al., Aquaculture and Fisheries, https://doi.org/10.1016/j.aaf.2019.02.001
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uncertainty of estimates with respect to key model parameters can be quantified by running Monte Carlo simulation. This method was mainly applied to some American fisheries, such as fisheries managed by the South Atlantic Fishery Management Council and the Mid-Atlantic Fishery Management Council (Carruthers et al., 2014). This method has also been used for the U.S. west coast groundfish (Wetzel & Punt, 2015). Billfishes (the collective name for marlins, sailfishes, and shortbill Spearfishes) are large, swiftly swimming, epipelagic, apex ocean predators (Habegger, 2014). Their morphological taxonomy was reviewed by Nakamura (1985) and a new genetics-based taxonomy given by Collette, Mcdowell, and Graves (2006). They are surface dwellers and distribute in shallower water (near-shore) (Young et al., 2011). During the summer, they move into productive warm-temperate waters for heavy feeding, and in autumn, they move back to tropical waters for overwintering and spawning (Chiang et al., 2006). In Indian Ocean, blue marlin is a billfish species with medium fishery data. The blue marlin occurs throughout tropical and subtropical waters of the Pacific, Atlantic and Indian Ocean (Nakamura, 1985). They are a bycatch species that require catch-effort statistics for stock assessments (Goodyear & Phillip, 2016). The Indian Ocean blue marlin was successfully assessed by IOTC WPB using state-space Bayesian production model (BSP-SS; IOTC-WPB14, 2016) and management advice was developed. Thus, our intention is to choose a candidate data poor method to Indian Ocean blue marlin and evaluate its reliability in developing management quantity. In this study, we applied the DCAC to Indian Ocean blue marlin to estimate sustainable yield (Ysust) and compared it with maximum sustainable yield (MSY) estimated by the state-space Bayesian production model. Stock assessment methods relying on different data and assumptions often lead to differences in estimates of management quantities. However, if the estimate of Ysust by DCAC is lower than MSY by BSP-SS, the Ysust can be regarded as precautionary management quantity and it suggests that the DCAC be a reliable data poor method in developing Ysust based management advice.
Fig. 1. Combined blue marlin catches in the IOTC database (1950–2015).
2001; Pine et al., 2008). The natural mortality was thus calculated to be 0.41 year−1. 2.3. Estimation methods 2.3.1. Basic equation of DCAC Normally, DCAC relied on the annual catch data, the relative decline in abundance (Δ), the natural mortality, and the ratio of FMSY (fishing mortality rate corresponding to MSY) to M (MacCall, 2009). Δ could be calculated by the relative reduction from the first year (FYR) to the last year (LYR) of the catch time series and its computation formula is as follows:
=
B MSY B0
n+
(
FMSY M
)M
1
(3)
Where ∑C is total catches, n is the length of the time series, B0 is virgin biomass, BMSY is biomass which produces MSY and BMSY/B0 is the biomass of the maximum Ysust relative to the carrying capacity. Restrepo et al. (1998) proposed the ratio of FMSY to M (c), so the Ysust is
Blue marlin is a bycatch species of tuna longline and gillnets fleets operating in the Indian Ocean and it is largely seen as a non-target species of industrial and artisanal fisheries. The main data required for DCAC method is total catch. In recent years, the fleet of Taiwan, China (longline) accounted for around 33% of total catches of blue marlin; and the fleet of Indonesia (fresh longline) and Pakistan (gillnet) accounted for around 28% and 14% of total catches, respectively (IOTCWPB14, 2016). Longline catches account for around 74% of total catches, followed by gillnets (23%), with remaining catches recorded under troll and handline fisheries (IOTC-WPB14, 2016). In this study, the combined catch data and two CPUE indexes from Japan and Taiwan, China of the blue marlin to be used by DCAC was downloaded from IOTC website (www.iotc.org) and time series of catch is 1950–2015 (Fig. 1).
Ysust =
C n+
(
B MSY cM B0
)
1
(4)
Input information includes the sum of catches and associated number of years, the relative reduction in biomass during that period, M, and the assumed ratio of FMSY to M (MacCall, 2009). With all these being set, the assessment with uncertainty was integrated by Monte Carlo simulation, and a random re-sampling was done 10,000 times in order to generate the probability distribution of Ysust. 2.3.2. Parameter setting Due to lack of accurate fishery data, Δ was unable to be precisely estimated. There is no clear value of Δ that can serve as a default and if nothing at all is known about the value of Δ, it may be appropriate to assume three parameters of different levels, 0.3, 0.5, 0.7 for precautionary purpose. Most fishery stock–recruitment relationships indicated that BMSY < 0.5B0, and according to various previous researches (Clark, 1991; NMFS, 1998; Restrepo et al., 1998), for most teleosts including blue marlin the ratio of BMSY to B0 is approximately 0.4. In this study, two levels of density dependence (0.4 and 0.6) were assumed for BMSY/B0. In some fishery cases with limited data, Thompson (1993) and NMFS (1996) suggested the assumption of c = 0.8 and c = 0.75.
2.2. Estimation of natural mortality Natural mortality rate (M) was obtained by the Pauly (1980)'s formula with growth parameter k, gradual length L (cm) and annual average surface temperature T, as shown below:
0.279 ln L + 0.6543 ln k + 0.463 ln T
(2)
C
Ysust =
2.1. Data resources
0.0152
BLYR B0
The DCAC provides an estimate of the yield (Ysust) that would keep the stock sustained:
2. Material and methods
ln M =
BFYR
(1)
Where L was 244 cm, and it was based on fitting von Bertalanffy growth curve to the size-at-age data of Prince, Lee, Zweifel, and Brothers (1991) and Wilson (1984). The growth parameters (k) was 0.28 year−1 which was obtained using Pine, Martell, Jensen, Walters, and Kitchell (2008). The SST was 26 °C as used in other study (Hinton, 2
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3. Results
Table 1 Specification of DCAC for Indian Ocean blue marlin. Δ
Bmsy/B0 = 0.4 c
0.3 0.5 0.7
3.1. Estimation of sustainable yield based on different parameter assumptions
Bmsy/B0 = 0.6
0.6
0.8
1.0
0.6
0.8
1.0
A1 B1 C1
A2 B2 C2
A3 B3 C3
A4 B4 C4
A5 B5 C5
A6 B6 C6
The probability distribution of Ysust is shown in Fig. 2. The maximum median of the estimate of Ysust is 6800 t and the minimum median is 6190 t. The estimation varied as low as 10% and the parameters had little influence on the estimate of Ysust in accordance with results from Fig. 3. The estimates for sustainable yield were not sensitive to the choices of Δ or c and the estimate of Ysust is about 6000 t to 7000 t (Fig. 3). The estimate of Ysust decreased lightly with the increase of depletion level (Δ), and increased lightly with the ratio of FMSY to M (Fig. 3). The sensitivity analysis to M showed that, M = 0.2 resulted in a lower estimate of Ysust and decreased over M = 0.41 by 5.05% (Fig. 4). The estimate of Ysust increased with the increase of M (Fig. 4). Ysust based on different parameter assumptions was lower than the MSY of 11,926 t by BSP-SS and the DCAC method appeared relatively robust to the different parameters.
Table 2 Specification of Δ based on CPUE data. Fleet of longline CPUE
Time window
Reduction in biomass (Δ)
Japan Japan Japan Japan Taiwan, China Taiwan, China Taiwan, China
1971–2015 1980–2015 1990–2015 2000–2015 1980–2015 1990–2015 2000–2015
0.45 0.58 0.06 0.07 −0.20 −0.53 −0.22
3.2. The influence of catch time series on the estimation of sustainable yield According to the catch data of the blue marlin in the Indian Ocean (1950–2015) (Fig. 1), the Ysust was estimated using different catch time series and a clearly increasing trend was observed depending on the data set. The minimum median of the estimate of Ysust is 6610 t when the 1950–2015 catch time series was selected. The median of the estimate of Ysust of about 9700 t is close to the MSY of 11,926 t by BSP-SS when catch time series for 1990–2015 and 2000–2015 were used (Fig. 5).
For Indian Ocean blue marlin, three different levels of c were assumed and a total of 18 models were considered (3 × 2 × 3 = 18). DCAC analysis was developed as shown in Table 1. MacCall (2009) suggested that in terms of natural mortality rate (M), the use of DCAC is not recommended if M is greater than ∼0.2 year−1, above which the depletion correction becomes small. In this paper, the M = 0.41 year−1 based on Equation (1), we also set a level of M = 0.2 year−1 to evaluate the sensitivity of estimates of Ysust to M. Ysust was estimated based on standardized CPUE time series from Japanese longline fishery (1971–2015) and Taiwanese longline fishery (1980–2015), respectively. We tested different sets of the same time series by decade and the assumed Δ is listed in Table 2. The time series block by decade was chosen subjectively.
3.3. Estimation of sustainable yield based on different CPUE series The probability distribution of blue marlin Ysust shown in Fig. 6 is based on two different CPUE indexes. There were some differences in the results based on the different CPUE time series and the estimate of Ysust increased when time series data was shortened. The minimum median of the estimate of Ysust was 7550 t based on the CPUE series of
Fig. 2. Frequency distribution of sustainable yield for blue marlin with Monte Carlo simulations. 3
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Fig. 3. Estimation of sustainable yield of Indian Ocean blue marlin using DCAC. Dashed lines stand for the average catch (1950–2015).
4. Discussion 4.1. Management implication of sustainable yield estimates Different assessment models rely on the same or different theories, hypotheses, types of data (including biological information, fisherydependent and -independent data) and statistical methods. Indian Ocean blue marlin was assessed by the state-space Bayesian production model in the Working Party of Billfish meeting in 2016 (IOTC-WPB14, 2016). The estimate of Ysust by DCAC was lower than MSY of 11,926 t by BSP-SS. This implied that the Ysust by DCAC could be regarded as precautionary management quantity and it suggests that the DCAC be a reliable data poor method in developing Ysust based management advice for Indian Ocean blue marlin. With data-rich methods (e.g., that estimate a stock-recruitment relationship) we can derive an estimate for MSY, however data-poor methods make a lot of assumptions and since we are not estimating any kind of stock recruitment relationship. We don't have the data to come up with an analytical “solution” for MSY so we are left with making an approximation with DCAC.
Fig. 4. Sensitivity analysis for the estimate of sustainable yield and natural mortality rate used in the DCAC model.
4.2. Implication of DCAC to other billfish species The majority of billfish stocks lack sufficient catch, survey, and other biological data to calculate current abundance and productivity using conventional stock assessment methods, requiring the use of alternative, data-limited methods (Carruthers et al., 2014). Other species such as Sailfish and Shortbill spearfish are considered as data-poor stocks (e.g. no reliable abundance index and size composition). Compared with other data sources, the data on catches can be considered as amongst the most reliable available for billfishes except when catches are known to be substantially underestimated (Hinton & Maunder, 2014). These billfishes are believed to be similar to blue marlin in terms of biology, fishery history and data pattern. Blue marlin was used to test whether the data-poor approach can be applied in billfishes. Result from this study suggested that DCAC can be used to estimate Ysust for Indian Ocean blue marlin, as shown by its conservative estimate of Ysust, compared with MSY by BSP-SS. If the reasonable time
Fig. 5. Sustainable yield of blue marlin estimated by DCAC based on different time series.
Japan (1971–2015) (Table 3). The median of the estimate of Ysust based on the CPUE series of Taiwan, China (1990–2015, 2000–2015) is over the MSY of 11,926 t by BSP-SS. 4
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Fig. 6. Distribution of sustainable yield estimated based on CPUEs from Taiwan, China, and Japan.
change in time series after catch increases. Common empirical methods for estimating M include formulas obtained by Pauly (1980), Hoenig (1983) and Jensen (1996) et al. Hinton (2001) calculates M values at 0.41 year−1 for males by Pauly (1980)'s method. In this paper, the natural mortality (M) is calculated as 0.41 year−1 by Pauly's method and it is almost similar to M = 0.38 year−1 (approx. 95% confidence interval 0.30–0.45 year−1) from the MULTIFAN-CL model in Kleiber, Hinton, and Uozumi (2003). The natural mortality used is quite a bit higher than that suggested by the MacCall (2009) paper and considering whether the depletion correction has an impact on the model, we compared the results of M = 0.2 and M = 0.41. The result shows the estimate of Ysust increased with the increase of M (Fig. 3) and variation trend of M is the same as that of parameter c, which is not sensitive to this model. The M = 0.4 resulting in a slightly higher estimate of Ysust compared with M = 0.2 by 5.05%, indicating that the influence of M on the result is minor for blue marlin even if we assumed a doubled value of M (Fig. 3). This study showed that DCAC could be used to estimate sustainable yield for the Indian Ocean blue marlin and consequently be used to give some management advice for this data-poor fishery. However, the results of this study should not be used directly to develop management advices, but use recent data and follow recommendations from the IOTC scientific commission before its practical applicability. In addition, its applicability remains to be further studied in the case of data mis-reporting and/or non-reporting.
Table 3 Sustainable yield of blue marlin estimated by DCAC based on different CPUEs. Data source
Time Series
Mean/1000t
Median/1000t
Japan Japan Japan Japan Taiwan, China Taiwan, China Taiwan, China
1971–2015 1980–2015 1990–2015 2000–2015 1980–2015 1990–2015 2000–2015
7.30 7.93 10.81 12.38 11.01 19.25 22.09
7.55 8.27 10.64 11.27 9.68 12.74 12.83
series and Δ was considered, DCAC is reliable for blue marlin in deriving precautionary management quantity, which can provide management advice in term of catch limit. Also, if the conventional stock assessments cannot be conducted, data-poor approaches such as the DCAC could be applied to other billfishes and their uncertainty be estimated for sustainable yield. 4.3. Sensitivity to assumptions In this study, the estimate of Ysust by DCAC was lower than the provisional reference point of 11,704 t by the management proposal. This suggested that the Ysust estimated by DCAC was more conservative. Ysust of about 6300 t by 18 DCAC analyses (1950–2015 catch time series) is not very sensitive to the parameters and appears relatively robust to the different parameters (Fig. 2). According to MacCall (2009) and Geng et al. (2017), Ysust will increase with c, and the probability distribution can gradually reach stable with the increase of c, which is consistent with the results of this study. The choice of time series has great influence on DCAC results. Considering the great changes in the catch data of the blue marlin in the Indian Ocean (1950–2015) (Fig. 1), we tested different catch time series. There were significant differences between the estimations of Ysust based on each of the five catch series. The estimate of Ysust increased gradually with the decrease of the time series and tended to reach stable after 1980. The estimates of Ysust were both about 9000 t for 1980–2015 and 1990–2015, which was closer to the MSY estimated by the BSP-SS. In terms of time series, we recommend the use of time series after 1980, with small sensitivity. The Δ values of Taiwanese fleets were negative and hence we simulated based on the standardized CPUE submitted by Japan longline fleets (1971–2015) and the standardized CPUE submitted by Taiwan, China longline fleets (1980–2015). Which the evaluation results of the Japanese group are the most optimistic, sustainable yield is evenly distributed. The relative reduction of Taiwanese group is negative (Δ ≤ −0.2), and susceptible to extreme value (1990–2015, 2000–2015), and short time series, reduces the DCAC model fault tolerance, which is easy to produce abnormal results (Geng et al., 2017). Based on the above analysis, the estimate of Ysust based on the CPUE of Japan (1980–2015) was reliable. Similarly, the best fit for time series would be the section where sudden
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