PROJECTIONS, KOBE PLOTS, AND MAXIMUM SUSTAINABLE YIELDS FOR ATLANTIC BIGEYE TUNA 2015

Transcription

1 SCRS/2015/168 Collect. Vol. Sci. Pap. ICCAT, 72(2): (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 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 ( ). 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 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 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 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 ( ). 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 t continúan, no está previsto que el stock se recupere hasta B/B RMS >1 con al menos un 50% de probabilidades antes de 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 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 ( ). 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, , USA. Michael.Schirripa@noaa.gov 564

2 KEYWORDS Bigeye tuna, stock assessment, yield predictions 1. Introduction The meeting of the 2015 ICCAT bigeye tuna stock assessment session was held in July 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 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 and with estimates of F/ FMSY ranging from to 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

3 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 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 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 ( ). 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

4 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 ~ References Anon 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 Variability of fishing mortality by age: consequences for maximum sustainable yield. North American Journal of Fisheries Management 16: Maunder, M.N The relationship between fishing methods, fisheries management and the estimation of maximum sustainable yield. Fish and Fisheries, 3: Schirripa, M.J. In press. SCRS/2015/126. An assessment of Atlantic bigeye tuna for p. 567

5 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

6 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) Constant catch projections Probability of Underfished (B>Bmsy) TAC(000t) Constant catch projections Probability of being in the green zone (B>Bmsy and F<Fmsy) TAC(000t)

7 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

8 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

9 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

10 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

11 MT Fishing Mortality Age (yrs) MT Figure 6. Percentage of catch by major gear group for Atlantic bigeye tuna Minimum Age in Catch 130, , , ,000 90,000 80,000 Total Yield at MSY Year 70, Year 650, , , ,000 SSB at MSY Fmsy 450, Year 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

12 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

13 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