SCRS/2015/168 Collect. Vol. Sci. Pap. ICCAT, 72(2): 564-576 (2016) PROJECTIONS, KOBE PLOTS, AND MAXIMUM SUSTAINABLE YIELDS FOR ATLANTIC BIGEYE TUNA 2015 Michael J. Schirripa 1 SUMMARY This work is intended to accompany the 2015 bigeye tuna assessment by providing projections, KOBE plots and estimates of maximum sustainable yield for the work done within the Stock Synthesis framework. The combined model estimates the probability of fishing mortality in 2015 being greater than F MSY of 80% and biomass being less B MSY of 99 percent. If the current catches of approximately 70,000 mt are continued the stock is not projected to rebuild to B/B MSY > 1 with at least a 50% probability by 2028. To rebuild to B/B MSY > 1 with at least 50% probability by 2026 (i.e. ten years) would require a total allowable catch of no greater than 60,000 mt. The constant catch projections of B/B MSY and F/F MSY provided assume that the proportion of catch from each fleets will remain constant within the future time frame considered (2015-2028). However, this assumption is not well supported by the historic trends. As the fishery continues to focus on increasing younger fish the year specific estimates of MSY decrease while the stock size required to achieve the lower MSY increases. RÉSUMÉ Ce travail est destiné à accompagner l'évaluation de 2015 du thon obèse en fournissant des projections, des diagrammes de Kobe et des estimations de la production maximale équilibrée pour le travail accompli dans le cadre de Stock Synthèse. Le modèle combiné estime la probabilité selon laquelle la mortalité par pêche en 2015 est supérieure à 80 % de F PME et la biomasse est inférieure à 99 % de B PME. Si les captures actuelles d'environ 70.000 t étaient maintenues, selon les projections, le stock ne se rétablirait pas à B/B PME > 1 avec au moins 50 % de probabilités d'ici à 2028. Pour que le stock se rétablisse à B/B PME > 1 avec au moins 50 % de probabilité d'ici à 2026 (c'est-à-dire en dix ans), la prise totale admissible ne devrait pas dépasser 60.000 t. Les projections de capture constante de B/B PME et F/F PME fournies postulent que la proportion des prises de chaque flottille restera constante dans le futur cadre temporel considéré (2015-2028). Toutefois, ce postulat n'est pas bien étayé par les tendances historiques. Alors que la pêcherie continue à se concentrer sur des poissons de plus en plus jeunes, les estimations spécifiques à l'année de la PME diminuent tandis que la taille du stock nécessaire pour atteindre une PME plus faible augmente. RESUMEN Este trabajo pretende apoyar la evaluación de patudo de 2015 proporcionando proyecciones, diagramas de Kobe y estimaciones del rendimiento máximo sostenible para el trabajo realizado en el marco de Stock Shynthesis. El modelo combinado estima la probabilidad de que la mortalidad por pesca en 2015 fuera superior al 80% de la F RMS y de que la biomasa fuera inferior al 99% de la B RMS. Si las capturas actuales de aproximadamente 70.000 t continúan, no está previsto que el stock se recupere hasta B/B RMS >1 con al menos un 50% de probabilidades antes de 2028. Para recuperarse hasta B/B RMS >1 con al menos un 50% de probabilidades antes de 2026 (es decir, diez años) se requeriría un total admisible de capturas no superior a 60.000 t. Las proyecciones proporcionadas de captura constante de B/B RMS y F/F RMS asumen que la proporción de captura de cada una de las flotas permanecerá constante en el periodo futuro considerado (2015-2028). Sin embargo, este supuesto no está respaldado por las tendencias históricas. A medida que la pesquería continúa centrándose en peces cada vez más jóvenes, las estimaciones específicas del año de RMS descienden, mientras que el tamaño de stock requerido para lograr el RMS menor aumenta. 1 NOAA Fisheries, Southeast Fisheries Center, Sustainable Fisheries Division, 75 Virginia Beach Drive, Miami, FL, 33149-1099, USA. Email: Michael.Schirripa@noaa.gov 564
KEYWORDS Bigeye tuna, stock assessment, yield predictions 1. Introduction The meeting of the 2015 ICCAT bigeye tuna stock assessment session was held in July 2015. One of the modeling platforms requested to be used was the Stock Synthesis (SS) framework. Details of this model are given in Schirripa, 2015 (in press). No projections were done for the SS model due to a lack of time. However, projections inputs and specifications were discussed and the Group agreed to run stochastic projections using 12 scenarios agreed during the meeting encompassing the structural uncertainty of the current SS3 assessment (Table 1). 2. Methods Projections were made for each of the twelve models by fixing the catch at the levels specified during the assessment meeting: 0 and 40,000-100,000 mt in increments of 5,000 mt. Future recruitments were taken directly from the stock recruitment function assigned to that model configuration. For a complete description of each of the twelve model configurations see Report of the Stock Assessment Group (Anon., 2015 (in press)). Uncertainty in the estimate of the current and projected status of the stock was characterized using a combination of within and between model variations. For within model variation I used the mean and standard deviations of the estimates of F/ F MSY and B/ B MSY as estimated by the hessian matrix. To characterize between models variation a Monte-Carlo approach was used. The mean and standard deviation of F/ FMSY and B/ BMSY for each year was used to generate three thousand random draws from a normal distribution for each of the twelve models. The mean of all random values of B/ B MSY and F/ F MSY across all twelve models (possible states of nature, n=36,000) was used to characterize the uncertainty of a single combined state-of-nature. Three values for Maximum sustainable yield (MSY) were calculated. The first single value used the last years (2015) estimate of gear specific selectivities and catch allocations. This is the value typically reported for assessment purposes and is referred to here as the current MSY. The second set of values of MSY was calculated on a year specific basis, which used each individual year s selectivity and catch allocation between fleets. This is referred to here as the year specific MSY. A third set of values of MSY was calculated on an age specific basis by assuming knife edge selectivity at each age and full selectivity for each age beyond. This is referred to here as the knife edge selectivity MSY KES. This is not to be confused with global MSY, which is calculated by considering only one, or at the most two, ages in the harvest (Maunder, 2002). 3. Results The derived quantities from the twelve scenarios are given in Table 1. The mean and standard deviation of each of the twelve SS models area given in Table 2. Estimates of B/ BMSY ranged from 0.435 and 0.917 with estimates of F/ FMSY ranging from 0.435 to 0.766. The model that estimated the stock to be the least productive was model 1, while the model that estimated the stock to be the most productive was model 12. The Kobe plot with snail tracks depicting all twelve scenarios resulted in B/ BMSY and F/ FMSY crossing into either the red or yellow zone in approximately 1992 with both values remaining in either the red zone or the yellow zone in 2014 (Figure 1). Likewise, the Kobe plot depicting all twelve scenarios in 2014 with uncertainty having all but three of the twelve scenarios fully in the red zone (overfished and overfishing) (Figure 2). When all twelve of the scenarios are combined into one scenario with uncertainty 67% of the points fall within the red zone, 32% in the yellow, and 1% in the green (Figure 3). Projections of the point estimates of BMSY and FMSY for the combined model scenario for each catch level is shown in Figure 4 and 5, respectively. These plots show that any catch levels above approximately 80,000 mt will not allow the stock to grow from its current level. In order for the stock to reach a B/ BMSY of > 1 within ten years (2026) would require a catch level less than 65,000 mt. 565
For the combined scenarios, to achieve at least a 50% probability (63%) of B/ BMSY > 1 with no fishing would take until 2020 (Table 3). To achieve at least a 50% probability (54%) of B/ BMSY > 1 in ten years (2026) would require a constant catch of no more than 60,000 metric tons. The decision table (Table 4) depicts the outcome of the management benchmarks B/ BMSY and F/ FMSY that could be expected under various pairing the total allowable catch (TAC) and alternative states of nature (least productive, combined, and most productive). The catch levels (0, 60,000 and 90,000 mt) are the levels that would allow each of the three states of nature to have at least a 50% probability of rebuilding to B/ BMSY > 1 in ten years (2026). If the least productive state of nature (model 1) is assumed for management then rebuilding B/ BMSY > 1 with at least a 50% (97%) probability in ten years would require a TAC of 0 mt for seven years. However, if the true productivity of the stock is closer to that depicted by the combined model and the TAC of 0 mt is used then rebuilding B/ BMSY > 1 with at least a 50% (63%) probability would occur in 2020. If the true productivity of the stock is closer to the most productive state of nature and a catch of 0 mt is used then rebuilding B/ BMSY > 1 with at least a 50% (87%) probability would occur in 2018. However, if the true productivity of the stock is assumed to be similar to the most productive (model 12), but is in fact more like the combined productivity, then the 90,000 mt catch level would result in the probability of B/BMSY > 1 in 2020 of only 15% and would not reach greater than a 50% probability within the time frame examined. In this way, the consequences of being wrong about which of the states of nature of the stock productivity can be made clear. The proportion of bigeye tuna landed by the three major groups (longline, bait boat, and purse seine) has changed considerably over time (Figure 6). Purse seine gear has accounted for an increasing portion of the catch since its inception in 1968 while the proportion from both longline and bait boat have declined. These trends have led to a decrease in the minimum age of the catch from age 4 in 1950 to approximately age 1.5 in 2014 (Figure 7). As a consequence of this shift to smaller fish, the year specific MSY has declined from a high of approximately 120,000 mt in 1965 to a low of approximately 85,000 in 2014, a nearly 30% decline. Furthermore, during this time the spawning stock biomass required to achieve the lower MSY has increased, but the fishing mortality to achieve MSY (FMSY) has remained more stable. However that same FMSY produces less yield from a necessarily larger stock. If the estimate of fishing mortality in 2014 is compared to the FMSY from 1962 (rather than 2014) then the status of stock is experiencing higher overfishing (Figure 8). Likewise, if the estimate of spawning stock biomass in 2014 is compared to the BMSY from 1962 (rather than 2014) then the status of stock is more over fished (Figure 8). Another perspective on MSY is referred to here as the MSY KES. This is the absolute maximum MSY that could be achieved if the fishery were prosecuted perfectly with a full, knife edge age-based selectivity at a particular reference age and full selectivity for ages greater than the reference age. At full selectivity at age 1+ the MSY KES is near its lowest levels and the fishing mortality required to -achieve MSY KES at its highest (Figure 9). Conversely, FMSY is lowest and MSY KES and BMSY highest at age of full selectivity at the oldest ages, ages 7 plus. These results are consistent with those reported in Goodyear, 1996, where it was shown that not only was the MSY in biomass highest when the oldest ages were selected, but also that the MSY in numbers was lowest at this same point. 4. Discussion If the current catches of approximately 70,000 mt are continued the bigeye tuna stock is not projected to rebuild to B/BMSY > 1 with at least a 50% probability by 2028, the last year of the projections. To rebuild to B/BMSY > 1 with at least a 50% probability by 2026 (i.e. ten years) would require a total allowable catch of no greater than 60,000 mt. The constant catch projections of B/B MSY and F/F MSY provided in this document assume that the proportion of catch from each of the fleets will remain constant within the future time frame considered (2015-2028). This assumption is not well supported by the historic trends also presented here. If the trend of increasing purse seine catch (relative to the other gear types) continues to increase the time required to rebuild the stock will increase as well. The purse seine fishery continues to make up a greater and greater proportion of the catch. If this trend continues the MSY estimates for this stock will continue to decrease and the stock size needed to achieve the lower MSY will increase. In this way the management of the bigeye stock may be experiencing benchmark drift. As the fishery continues to focus on younger and younger fish the management targets continue to drift and requiring a lower and lower total allowable catch to achieve the management objectives. As surplus production models, such as ASPIC, assume full and constant selectivity for all ages over the entire time period of consideration these types of models are inappropriate for fisheries with mixed and time varying selectivities, such as bigeye tuna and yellowfin tuna. 566
While the MSY KES is very likely unachievable based on the unlikely meeting of the strict assumptions involved (knife edge age-based selectivity) it does provide a valuable perspective. The difference between the MSY KES and the current MSY demonstrates an efficiency factor of the fishery. If the F MSY from the MSY KES were used to calculate the F/F MSY benchmark the stock would be undergoing sever overfishing (F/F MSY ~ 5.0). If B MSY from the MSY KES were used the estimate of B/B MSY in 2014 would be ~ 0.40. References Anon. 2016. In press. SCRS/2015/015. Report of the 2015 ICCAT Bigeye Tuna Stock Assessment Session (Madrid, Spain, July 13 to 17): 61p. Goodyear, C.P. 1996. Variability of fishing mortality by age: consequences for maximum sustainable yield. North American Journal of Fisheries Management 16: 8-13. Maunder, M.N. 2002. The relationship between fishing methods, fisheries management and the estimation of maximum sustainable yield. Fish and Fisheries, 3: 251-260. Schirripa, M.J. In press. SCRS/2015/126. An assessment of Atlantic bigeye tuna for 2015. 13p. 567
Table 1. The twelve scenarios (states of nature) agreed upon for the Stock Synthesis model. For more details see Anon., 2015 (in press). Table 2. Point estimates for the mean/standard deviations of B/B MSY and F/F MSY for the twelve scenarios agreed upon for the Stock Synthesis model. B/Bmsy F/Fmsy MODEL Mean Std Dev Mean Std Dev 1 0.435 0.018 1.635 0.067 2 0.538 0.022 1.318 0.055 3 0.727 0.033 0.997 0.044 4 0.518 0.021 1.509 0.070 5 0.653 0.029 1.171 0.058 6 0.864 0.039 0.878 0.044 7 0.474 0.023 1.443 0.075 8 0.589 0.030 1.161 0.061 9 0.782 0.044 0.887 0.050 10 0.552 0.027 1.316 0.075 11 0.703 0.037 1.008 0.062 12 0.917 0.052 0.766 0.050 568
Table 3. Probability of the events F < F MSY (top), B > B MSY (middle) both events (bottom) by year and constant catch level for the combined scenario. Constant catch projections Probability of Underfishing (F<Fmsy) TAC(000t) 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 0 20 100 100 100 100 100 100 100 100 100 100 100 100 100 40 20 86 91 94 96 97 98 98 99 99 99 100 100 100 45 20 75 84 88 91 93 95 96 96 97 98 98 98 99 50 20 65 76 82 86 89 91 93 95 96 97 98 98 99 55 20 56 67 73 77 81 84 86 88 90 91 93 94 95 60 20 45 57 63 68 72 75 78 80 82 84 86 87 88 65 20 36 48 54 59 63 66 69 72 74 76 78 79 81 70 20 28 39 46 50 54 57 60 63 65 66 67 69 70 75 20 21 32 37 39 44 48 51 54 55 57 59 59 60 80 20 16 25 30 34 37 40 43 45 46 49 47 47 47 85 20 11 20 24 27 30 33 34 36 35 38 38 39 40 90 20 8 15 19 21 23 25 26 27 28 29 28 29 27 95 20 5 11 15 16 18 19 20 20 19 20 18 17 22 100 20 3 9 11 12 13 14 14 12 13 13 13 14 14 Constant catch projections Probability of Underfished (B>Bmsy) TAC(000t) 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 0 1 0 2 15 41 63 79 90 95 98 99 99 100 100 40 1 0 0 5 18 32 44 54 62 69 75 80 84 87 45 1 0 0 4 16 28 39 48 56 63 69 74 78 81 50 1 0 0 3 13 25 35 43 50 57 63 68 73 76 55 1 0 0 3 11 22 30 38 45 51 57 61 66 70 60 1 0 0 2 10 18 26 32 38 44 49 54 58 62 65 1 0 0 2 8 15 22 28 33 38 43 47 51 54 70 1 0 0 1 7 13 18 23 28 32 36 40 43 46 75 1 0 0 1 5 11 15 20 23 27 30 33 36 38 80 1 0 0 1 4 9 12 16 19 22 25 27 29 32 85 1 0 0 1 3 7 10 13 15 18 20 22 24 25 90 1 0 0 0 3 5 8 10 12 13 15 16 18 18 95 1 0 0 0 2 4 6 8 9 10 11 12 13 13 100 1 0 0 0 2 3 5 6 6 7 8 8 9 9 Constant catch projections Probability of being in the green zone (B>Bmsy and F<Fmsy) TAC(000t) 2015 2016 2017 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 0 1 0 2 15 41 63 79 90 95 98 99 99 100 100 40 1 0 0 5 18 32 44 54 62 69 75 80 84 87 45 1 0 0 4 16 28 39 48 56 63 69 74 78 81 50 1 0 0 3 13 25 35 43 50 57 63 68 73 76 55 1 0 0 3 11 22 30 38 45 51 57 61 66 70 60 1 0 0 2 10 18 26 32 38 44 49 54 58 62 65 1 0 0 2 8 15 22 28 33 38 43 47 51 54 70 1 0 0 1 7 13 18 23 28 32 36 40 43 46 75 1 0 0 1 5 11 15 20 23 27 30 33 36 38 80 1 0 0 1 4 9 12 16 19 22 25 27 29 32 85 1 0 0 1 3 7 10 13 15 18 20 22 24 25 90 1 0 0 0 3 5 8 10 12 13 15 16 18 18 95 1 0 0 0 2 4 6 8 9 10 11 12 13 13 100 1 0 0 0 2 3 5 6 6 7 8 8 9 9 569
Table 4. Decision table for Atlantic bigeye tuna showing the probabilities of B>B MSY and F>F MSY for three levels of Total Allowable Catch (TAC), the least productive model, all models combined, and the most productive model. TACs considered are those that will have a probability of B>B MSY within ten years (by 2026). Table shows the projected status of the stock if the catches are matched (diagonal of blocks moving from upper left to lower right) or mismatched (all other blocks) with the three models (states of nature). Least Productive Most Productive MODEL 1 Combined MODEL 12 TAC Year Pr B>Bmsy Pr F<Fmsy Pr B>Bmsy Pr F<Fmsy Pr B>Bmsy Pr F<Fmsy 0 2015 0 0 1 20 6 100 0 2016 0 100 0 100 2 100 0 2017 0 100 2 100 25 100 0 2018 0 100 15 100 87 100 0 2019 0 100 41 100 96 100 0 2020 2 100 63 100 98 100 0 2021 22 100 79 100 99 100 0 2022 53 100 90 100 100 100 0 2023 75 100 95 100 100 100 0 2024 88 100 98 100 100 100 0 2025 94 100 99 100 100 100 0 2026 97 100 99 100 100 100 0 2027 99 100 100 100 100 100 0 2028 99 100 100 100 100 100 60 2015 0 0 1 20 6 101 60 2016 0 0 0 45 2 100 60 2017 0 5 0 57 2 100 60 2018 0 10 2 63 23 100 60 2019 0 13 10 68 56 100 60 2020 0 17 18 72 71 100 60 2021 0 21 26 75 79 100 60 2022 0 24 32 78 84 100 60 2023 0 27 38 80 88 100 60 2024 0 30 44 82 91 100 60 2025 1 32 49 84 93 100 60 2026 2 35 54 86 94 100 60 2027 4 37 58 87 96 100 60 2028 7 38 62 88 96 100 90 2015 0 0 1 20 6 100 90 2016 0 0 0 8 2 43 90 2017 0 0 0 15 0 55 90 2018 0 0 0 19 4 59 90 2019 0 0 3 21 20 62 90 2020 0 0 5 23 31 66 90 2021 0 0 8 25 38 68 90 2022 0 0 10 26 44 71 90 2023 0 0 12 27 48 73 90 2024 0 0 13 28 51 75 90 2025 0 0 15 29 54 77 90 2026 0 0 16 28 56 79 90 2027 0 0 18 29 59 81 90 2028 0 0 18 27 61 83 570
Figure 1. Kobe phase plot for all twelve SS scenarios considered. Figure 2. Comparison of 2015 F/F MSY and B/B MSY for all twelve SS scenarios considered. 571
Figure 1. Kobe phase plot for all twelve SS configuration combined with uncertainty for 2015 and percentage of points (not shown) within each color quadrant. 572
Figure 4. Projected B/B MSY given fixed catch levels for all twelve SS configurations combined. Figure 5. Projected F/F MSY given fixed catch levels for all twelve SS configurations combined. 573
MT Fishing Mortality Age (yrs) MT Figure 6. Percentage of catch by major gear group for Atlantic bigeye tuna. 5 4 3 2 1 Minimum Age in Catch 130,000 120,000 110,000 100,000 90,000 80,000 Total Yield at MSY 0 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 Year 70,000 1962 1967 1972 1977 1982 1987 1992 1997 2002 2007 2012 Year 650,000 600,000 550,000 500,000 SSB at MSY 0.25 0.20 0.15 0.10 0.05 Fmsy 450,000 1962 1967 1972 1977 1982 1987 1992 1997 2002 2007 2012 Year 0.00 1962 1967 1972 1977 1982 1987 1992 1997 2002 2007 2012 Year Figure 7. Minimum age of catch by year (upper left); year specific maximum sustainable yield (upper right); year specific spawning stock biomass at maximum sustainable yield (lower left); and fishing mortality at year specific maximum sustainable yield (lower right). 574
Figure 8. Fishing mortality over fishing mortality that produces maximum sustainable yield (top) and biomass over biomass that produces maximum sustainable yield (bottom) assuming selectivity and gear specific catch allocations for 1962 (blue) and 2014 (red) for Atlantic bigeye tuna. 575
Figure 9. Fishing mortality that produces maximum sustainable yield (top) and maximum sustainable yield (bottom, blue) and spawning stock biomass that produces maximum sustainable yield (bottom, red) as a function of age at full knife edge selectivity for Atlantic bigeye tuna. 576