stock assessment approaches and their data ... - CiteSeerX

SCRS/2001/055

Col.Vol.Sci.Pap. ICCAT, 54 (2): 377-389. (2002)

STOCK ASSESSMENT APPROACHES AND THEIR DATA REQUIREMENTS FOR DEALING WITH MIXING OF WESTERN AND EASTERN NORTH ATLANTIC BLUEFIN TUNA: A BAYESIAN PERSPECTIVE M.K. McAllister 1 and E.A. Babcock2 SUMMARY This paper evaluates the potential merits of alternative stock assessment approaches and their data requirements to dealing with the mixing of western and eastern North Atlantic bluefin tuna stocks. A Bayesian statistical perspective is adopted to evaluate existing approaches and formulate additional ones that could make the best use of available data to provide fisheries management advice in light of the current uncertainties over stock mixing. Indications of the additional data required for the various stock assessment approaches are also provided. A scenario – based assessment approach is advocated in which plausible alternative models are fitted to the available data and the weight of evidence is evaluated in light of the existing data for each alternative. Bayes' factors are advocated for this purpose. The potential consequences of alternative management approaches should be evaluated under each scenario keeping in mind the weight of evidence in support of each plausible alternative model for mixing. This approach is similar to that recently taken, except that the alternative hypotheses should be widened to include stock mixing alternatives. Evaluation of the frequency distributions of size and maturity at age in the Mediterranean and Gulf of Mexico and 2+ years delay pop-up archival tagging of mature fish appear to be among the most useful additional data that could reduce stock mixing uncertainties.

RÉSUMÉ Le présent document évalue les mérites potentiels d’approches alternatives d’évaluation du stock et leurs besoins en données pour traiter des échanges entre les stocks est et ouest de thon rouge de l’Atlantique nord. Une perspective statistique bayésienne est adoptée pour évaluer les approches existantes et en formuler d’autres susceptibles d’utiliser au mieux les données disponibles pour fournir des avis de gestion de la pêche au vu des incertitudes actuelles concernant les échanges entre stocks. Les données additionnelles requises pour les différentes approches de l’évaluation de stock sont également indiquées. Une approche d’évaluation basé sur des scénarios est avancée, dans laquelle des modèles alternatifs plausibles sont ajustés aux données disponibles et le poids de l’évidence est évalué d’après les données existantes pour chaque alternative. Les facteurs de Bayes sont avancés dans ce but. Les conséquences potentielles d’alternatives de gestion devraient être évaluées selon chaque scénario en gardant à l’esprit le poids de l’évidence étayant chaque modèle alternatif plausible de mélange. Cette approche est semblable à celle qui a été suivie récemment, si ce n’est que les hypothèses alternatives devaient être étendues pour inclure des alternatives de mélange entre stocks. L’évaluation de la distribution des fréquences de taille et de maturité à l’âge dans la Méditerranée et le golfe du Mexique, et du délai de 2+ ans des marques-archives pop-up apposées sur des poissons matures, semble être l’une des donnés additionnelles les plus utiles susceptibles de réduire les incertitudes concernant les échanges entre les stocks.

RESUMEN Este documento evalúa las ventajas potenciales de enfoques alternativos de evaluación de los stocks y sus requisitos de datos para abordar el tema de la mezcla entre los stocks este y oeste de atún rojo del Atlántico norte. Se ha adoptado una perspectiva estadística bayesiana para evaluar lo enfoques existentes y formular otros nuevos que saquen el máximo partido de los datos disponibles para proporcionar asesoramiento para la ordenación de las pesquerías a la luz de las actuales incertidumbres sobre la mezcla entre stocks. También se proporcionan indicaciones sobre datos adicionales necesarios para los diferentes enfoques de evaluación del 1

Renewable Resources Assessment Group, Department of Environmental Science and Technology, Imperial College, Room 4.89 Royal School of Mines, Prince Consort Road, London SW7 2BP United Kingdom. [email protected]. 2 Wildlife Conservation Society, Marine Conservation Program. 2300 Southern Blvd. Bronx, NY 10460 USA.

stock. Se favorece un enfoque de evaluación basado en escenarios, en el cual los modelos alternativos plausibles se ajustan a los datos disponibles y el peso de las pruebas se evalúa a la luz de los datos existentes para cada alternativa. Para este fin se aboga por los factores bayesianos. Las consecuencias potenciales de enfoques de ordenación alternativos deben evaluarse en cada escenario teniendo siempre en cuenta el peso de las pruebas sobre las que se fundamenta cada modelo alternativo plausible de mezcla. Este enfoque es similar al recientemente adoptado, con la diferencia de que las hipótesis alternativas deben ampliarse para incluir alternativas de mezcla entre stocks. La evaluación de las distribuciones de frecuencia de talla y maduración por clase de edad en el Mediterráneo y en el Golfo de Méjico y un plazo de más 2 + años de las marcas archivo “pop up” colocadas en peces maduros parecen ser los datos adicionales más útiles a la hora de reducir las incertidumbres sobre la mezcla entre stocks.

KEYWORDS Bluefin tuna, stock mixing, stock assessment, fishery management, Bayesian methods

INTRODUCTION ICCAT currently holds assessments of eastern and western North Atlantic bluefin tuna separately and no stock-mixing is assumed in these assessments. The stock boundary line is assumed to be at 45o longitude west. Additional modeling has been conducted since 1993 to evaluate the potential consequences of stock mixing for fisheries management of these North Atlantic tunas (Butterworth and Punt 1994; Porch and Turner 1999; Porch et al. 2001). Biological studies have also been conducted to provide information about the potential for stock-mixing and stock differentiation between the eastern and western North Atlantic including studies using conventional, pop-up and archival tags, DNA studies, maturity studies, and so on. As yet considerable controversy remains over the extent of stock differentiation, patterns of migration, the existence of spawning areas in addition to the Gulf of Mexico and the Mediterranean, and the extent of site fidelity of spawners. Modeling work has suggested that assessment results and TAC policy projection results can vary considerably depending on the scenario assumed. This paper evaluates the potential merits of alternative stock assessment approaches and their data requirements to dealing with the mixing of western and eastern North Atlantic bluefin tuna stocks. A Bayesian statistical viewpoint is adopted to evaluate existing approaches and formulate additional ones that could make the best use of available data to provide fisheries management advice in light of the current uncertainties over stock mixing. Indications of the additional data required for the various stock assessment approaches are also provided. Decision analysis as an approach to dealing with uncertainty in fisheries stock assessment Decision analysis has long been advocated as a rigorous approach to dealing with uncertainty in fisheries stock assessment (Walters and Hilborn 1976; Bergh and Butterworth 1987; Francis and Shotton 1997; Punt and Hilborn 1997; McAllister et al. 2000) and has recently been advocated in ICCAT stock assessments (McAllister et al. 2000, 2001). This approach efficiently organizes scientific efforts to inform decision makers about the potential consequences of alternative management choices that can be made. The approach is probabilistic and expresses outcomes as probability distributions and explicitly accounts for uncertainty in stock assessments by requiring the formal identification of alternative hypotheses or "scenarios" for fish stock dynamics (McAllister and Kirchner 2001). Alternative models are developed to represent these alternative scenarios and each is fitted to the data to estimate model parameters. Decision theory provides a number of ways to evaluate the relative plausibility of the various models (Koller 2000, French and Rios Insua 2000) based on the available data and expert judgement. For example, hierarchical decision methods such as the Analytic Hierarchy Process (Saaty 2000) allow information and values to be weighted by dividing the problem into a series of paired comparisons within a formalized hierarchy. Weightings based on

expert judgement have been used in fisheries (Butterworth et al. 1996, Suzuki 2001). Alternatively, Bayes' factors can be used to evaluate the plausibility of each model against the available stock assessment data. Probably the best use of the available information would be to give prior credibility ratings to the alternative models from expert judgement and qualitative information (Butterworth et al. 1996), then compute posterior probabilities for each alternative scenario using the stock assessment data. Decision analysis has been applied informally in some recent ICCAT stock assessments. For example in the 2000 assessment of the western north Atlantic bluefin tuna, two alternative scenarios were constructed for potential future recruitment series. One suggested that even if spawner biomass increased substantially, recruitment would not recover to former high levels before the 1970s because of changes in oceanographic conditions. The other scenario suggested that it could. The potential consequences of alternative TAC options were evaluated under each of these two alternatives and presented to ICCAT Commissioners to assist them in setting a TAC. The assessment explicitly gave equal weight to the two alternative recruitment scenarios (ICCAT 2000), thus conveying the uncertainty over them and allowing the Commissioners to make decisions based on this scientific judgment and modeling results obtained under the two alternative scenarios. In the sections below, a similar approach is suggested to formulate a stock assessment approach that can provide management advice that explicitly accounts for the alternative hypotheses for mixing between the eastern and western north Atlantic bluefin stocks and rigorously uses the available information to formulate this advice. Alternative hypotheses for mixing of the eastern and western north Atlantic tuna stocks Throughout the history of the Atlantic bluefin tuna fishery, many stock structure hypotheses have been suggested including separate stocks in the Mediterranean, Northeast Atlantic, Northwest Atlantic and Mediterranean, or a single Atlantic and Mediterranean stock (National Research Council, 1994). Several alternative hypotheses on stock mixing of northern Atlantic bluefin tunas have been formally considered in scientific work conducted for ICCAT. One implied by the current management protocol assumes that the stock boundary line between the eastern and western stocks of north Atlantic bluefin tuna is at 45o longitude west. Catches taken on either side of this boundary are assumed to come only out of the respective stock. Tagging data have suggested that many fish from each side cross this line. This has given rise to two other hypotheses that have been used to construct models of bluefin tuna mixing. One is the diffusion hypothesis which assumes that there is no spawning site fidelity and individual fish on each side cross over to the other and do not necessarily spawn where they were born (Porch and Turner 1999). The alternative "overlap" hypothesis assumes that fish may cross over to the other side of the ocean but exhibit absolute fidelity to the spawning sites where they were born. This has been considered to be more plausible than the diffusion model (ICCAT 1995), yet at least until recently, data have not been available to refute either hypothesis. Moreover, while these are two extreme hypotheses about mixing, other possibilities exist that involve, for example, more than two different breeding sites, and various combinations of the diffusion and overlap hypotheses. It is plausible that many fish that cross the ocean return to spawn only in the site where they were born but at the same time other fish might breed in spawning locations different from the one in which they were born. Some have also suggested that cross oceanic migrations could be episodic and caused by oceanographic fluctuations (Mather et al. 1995). Modeling studies have demonstrated that the assessment of resource abundance and projections for stock recovery are highly sensitive to assumptions about the presence of mixing (Butterworth and Punt 1994; Porch and Turner 1999, Porch et al. 2001). For example, estimates of abundance, especially the older age groups have been over twice as much when mixing models have been assumed (Porch and Turner 1999, Porch et al. 2001). Projections of stock recovery rates however are more pessimistic with the stock mixing models. Additionally, projection results are highly sensitive to whether diffusion or overlap mixing models are applied and to small changes in the mixing rates in each of these alternative models (Porch and Turner 1999). Therefore, the assessment of current status and the success of any TAC policy adopted in achieving stock building depend strongly on the stock

assessment model assumptions about mixing between east and west. It appears then that TAC advice should take into account uncertainty in the plausible alternative hypotheses on mixing by indicating the range of outcomes possible for each TAC option based on the plausible alternatives. As suggested above, the relative credibility of the alternatives hypotheses should also be assessed with the data available and data should be identified that could help to rigorously ascertain the correct mixing hypothesis. The next section discusses this issue. Data available versus required to evaluate the plausibility of alternative stock mixing hypotheses Data available on northern Atlantic bluefin tuna and their implications for the plausibility of alternative hypotheses on stock mixing have been considered in several recent ICCAT papers (Hester 2000; Lutcavage and Luckhurst 2001; Porch et al. 2001). Although considerable data have been collected, analyses of them do not currently allow ascertainment of which mixing hypothesis is the correct one. These data have been obtained using conventional, pop-up and archival tags, DNA studies, maturity studies, and so on. Table 1 summarizes the various data available, their implications for stock differentiation, and a few suggestions for further investigation. The most informative data about movements have come from conventional, archival and pop-up tagging of bluefin tunas in the northwest Atlantic and Mediterranean (Lutcavage et al. 2000; Block et al. 2000, 2001; De Metrio 2001, Yamashita and Miyabe 2001). Most recoveries of western conventional tagged fish have been west of 45o. 10% of western tagged fish have been recovered east of 45o longitude (Block et al. 2001). This is a cumulative percentage and does not reflect an annual rate of crossing. Additionally, this observation does not necessarily imply that 10% of fish in the west eventually cross 45o W to the eastern side. This is because the tag recovery rate in each part of the ocean depends on a variety of factors including the fishing effort in that part of the ocean and the tag reporting rate of fishermen fishing that part of the ocean. Take an extreme example. If 100% if the fishing effort was in the east, then 100% of all tags recovered would be east of 45oW, even if relatively few western fish (e.g., < 5%) crossed 45oW. Thus finding 10% tag recoveries in the east, of western tagged fish does not necessarily imply 10% of western fish cross to the east. Indeed, mixing models fitted to these data support annual movements rates east to west 1-4% and annual movements rates west to east of 0.3-4%, depending on the model (Porch et al. 2001). Analyses of these data suggest that the movement patterns vary for small, medium and large fish with large fish being the most mobile (Mather et al. 1995; Porch et al. 2001). Some large fish tagged with conventional tags in the northwest Atlantic have been recaptured in the Gulf of Mexico supporting the hypothesis of a feeding and spawning loop for western fish between these two locations. Most of the western fish archival tagged north of the Gulf of Mexico showed no visitation of tropical spawning grounds (Block et al. 2000, 2001) and the few recoveries of some of these in or on the entrance to the Mediterranean suggest that eastern breeding fish could feed in the west and spawn in the Mediterranean. A few large fish archival tagged in the northwestern Atlantic have shown visitations to the Gulf of Mexico supporting the idea that at least some Gulf of Mexico spawners feed in the northwest Atlantic. A few other spawning sized fish have been recorded to be south of Bermuda at during spawning months and in spawning temperature water suggesting the possibility of additional spawning areas for northwestern Atlantic fish. The satellite tagging data have indicated that 9-30% of large recovered tagged fish from the northwest Atlantic move east of 45o longitude during late winter and return west in late winter and fall (Block et al. 2001) and more recent analyses of these data suggest higher percentages visiting both sides of the Atlantic. However, for the archival tags recovered, the percentage of western tagged fish found to be visiting eastern waters does not necessarily imply that this is the percentage of western fish that visit the east. This is again because the percentage of tagged fish recovered east and west depends on a variety of factors including the fishing effort east and west. A few spawning sized individuals have been pop-up tagged in the Gulf of Mexico. None of these has been recorded east of 45o W. Pop-up tagging of Mediterranean fish indicated that many fish exited this sea and migrated to positions from 20o North to 75o North but no further west than 30o West (De Metrio et al. 2001).

Thus, none of these data can be used to rule out any of the mixing hypotheses except for the idea that fish from either side do not cross 45o W. The archival tags indicate that western fish are vulnerable to fishing pressures on both sides of the Atlantic (Block et al. 2000a, 2001). The observation that some northwestern Atlantic tagged fish visit the Gulf of Mexico and others visit the Mediterranean suggest a feeding zone in the Northwest Atlantic for both western and eastern spawners. No archival or pop-up tagged fish have yet been observed to show spawning visits to both the Gulf of Mexico and the Mediterranean (Block et al. 2001) and this lends some support to the spawning site fidelity hypothesis but the issue of spawning site fidelity is not resolvable with the current tagging data. Many additional observations of mature fish archival or pop-up archival tagged in the northwest Atlantic for longer time series of location recordings, e.g., over at least 2 to 4 years would provide a stronger test of the site fidelity hypothesis. Any observation of a fish making spawning visits to two different spawning sites would immediately refute the overlap hypothesis and support the diffusion hypothesis. This would still leave open the questions about the fractions of spawners that exhibit spawning site fidelity and the annual crossing rates (east to west and west to east) of those that do not. Large amounts of archival tagging data on mature fish at liberty for at least three years would be required to estimate this fraction. This is because the satellite tagged data suggest that the few mature fish followed over two spawning seasons have visited spawning grounds in only one of the two consecutive spawning seasons (Block et al. 2000, 2001). If large numbers of mature fish showed only complete spawning site fidelity over two or more visits to spawning grounds, this would strengthen support for the spawning site fidelity (two-stock overlap) hypothesis. This hypothesis test could be done using a model-based approach in which models representing alternative mixing and spawning site fidelity hypotheses were fitted to these data and fishing effort data for different oceanic regions to evaluate the probability of observing only fish with complete spawning site fidelity over two or more visits to spawning grounds under each alternative hypothesis. The DNA studies have shown equivocal results (Ely et al. 2001). No significant difference in mitochondrial DNA was found in 245 bluefin from the northwest Atlantic and the Mediterranean Sea. A preliminary study from 140 fish had indicated differences but these disappeared with the larger samples size. Fish of sizes between 127 and 190 cm and 197 and 277 cm were evaluated in both regions for differences. As the authors point out, null result does not necessarily imply a single panmictic stock. Cross oceanic migrations of fish that still return to the sites they were born are consistent with these results because fish could migrate across the ocean to feed but still return to the same site to spawn. Mitochondrial DNA or other DNA studies of pre-migratory juvenile (e.g., larval) bluefin tuna collected from the Mediterranean and Gulf of Mexico spawning sites would be a more effective control for the mixing of fish of migratory size and give a stronger test of the stock separation hypothesis. This would only be feasible if sufficiently large sample sizes of juvenile bluefin tuna could be obtained from the two known spawning sites. DNA samples from spawning adults could provide a similarly strong test of the spawning site fidelity hypotheses but the sample size required (a few hundred individuals from each location) would be nearly impossible to obtain. The 1998 detailed report on northern bluefin tuna (ICCAT 1999) states the following on age at maturity: "In the west, the age of first spawning of 8 years old is based on the size of fish in the Gulf of Mexico spawning area. In the East there is considerable evidence of a lower age of first spawning of age 5 [....]. It is a priority that detailed studies be conducted to determine the age of ogive maturity, given that a conclusive difference between the east and west Atlantic will be compelling support for a two stock hypothesis." Recent studies have suggested very different minimum sizes of maturity between the two areas, about 110 cm in the Mediterranean (Susca et al. 2001) and about 210 cm in the Gulf of Mexico (Block et al. 2000, 2001). However, differences in mean growth rates between fish in different regions could reflect differences in growth conditions and feeding habits of fish residing in them. This observation does not rule out some migrations of fish between spawning grounds, but does suggest a strong degree of segregation of fish between the west and east. A closer examination of the frequency distribution in size at age and age at maturity of fish in the Atlantic northwest, northeast, Gulf of Mexico and Mediterranean could potentially help to further elucidate the mixing of fish from different regions. The observation that spawning fish in each

spawning area exhibited non-overlapping distributions of growth rates and/or ages at maturity would lend strong support for the spawning site fidelity hypothesis. Considerable overlap in the frequency distributions for growth rate and age at maturity from different spawning grounds however could not be used to refute this hypothesis Taken together, these maturity and tagging data support the idea that at least two different biotypes exist for Atlantic bluefin tuna (Table 1). One is a population that spawns in the Mediterranean and has a smaller size and younger age of maturity. The other is a population that spawns in the Gulf of Mexico that has a larger size and older age of maturity. The feeding grounds of the eastern spawners extend to the north Atlantic ocean but the extent west is not certain. Archival tagging data support the possibility that eastern spawners migrate to and feed in the northwestern Atlantic. The eastwards extent of the feeding grounds of the western spawners is also uncertain but also extend east of 45o W, assuming that the fish tagged in the Northeast Atlantic were spawned in the Gulf of Mexico instead of being migrants from the Mediterranean. Additional data that could adequately test the spawning site fidelity hypothesis could include (1) genetic studies of pre-migratory juvenile bluefin tuna on the two spawning grounds, (2) archival tagging of a larger number of mature (spawning size) adults on the eastern and western spawning grounds to track interannual movements of larger numbers of mature fish, (3) pop-up archival tagging of mature fish with delays in tag pop-up of two or more years, if feasible, since most pop-offs have been programmed for up to 12 months after tagging (two or more years pop up would provide more information on spawning site fidelity), (4) studies to confirm the distribution of first ages at maturity on the two spawning grounds and (5) studies to confirm the frequency distribution of growth rates of Mediterranean and Gulf of Mexico spawners. A Bayesian viewpoint on current stock assessment protocols for eastern and western stocks The current ICCAT protocol for conducting assessments and providing management advice based on a 45oW dividing line between the eastern and western stocks and assuming that there is no mixing has appeared reasonable until recently. However, growing evidence suggests that its assumptions are not correct and the policy projections based on it could be misleading. As recent analyses of tagging data suggest oceanic annual crossing rates of at least 1%, models that incorporate such mixing rates would appear to be more appropriate for a baseline assessment model. If the assessment results happened to be little different whether mixing or no mixing was assumed, then the current modeling approach would serve as a suitable approximation. The problem is that the current ADAPT-VPA models with no mixing give very different assessments of stock status and policy projection results than the ones that include mixing (Butterworth and Punt 1994; Porch and Turner 1999) The question arises about which mixing model or models should be adopted to provide TAC advice? If there was little difference in results between the mixing model alternatives, for example, the diffusion and the overlap models, then it would not matter which one was adopted. While the estimates of stock status, e.g., abundance, differ little between the two mixing models (Porch et al. 2001), the policy projection results appear to be quite sensitive to which one is assumed (Porch and Turner 1999). Thus, it matters which mixing model is adopted for the provision of TAC advice. Model selection criterion such as the Akaike Information Criterion (AIC) that is based on the goodness of fit of the model to the data and down-weighted by the number of model parameters is one possibility that could assist in model choice (Porch et al. 2001). However, when the diffusion and overlap models are compared, using this criterion, conflicting results are obtained. The diffusion model is slightly more consistent with the tagging data and the overlap model is more consistent with the relative abundance series (Porch et al. 2001). Porch et al. (2001) fitted the diffusion and overlap models only to the conventional mark and recapture data up to and including 1997. The considerable archival tagging and pop up tagging data have not been included in the tagging data sets used. It would appear appropriate to fit these models to these additional tagging data to assist in the estimation of cross-oceanic migration rates and the evaluation of the plausibility of the two models. It remains to be seen whether the diffusion model is also more consistent with the pop-up tagging and archival tagging data sets. Thus, on this basis there is no compelling reason to reject either model and the

question arises, if both models are to be considered in the provision of management advice, how should their credibility be weighted? From a decision analytic point of view, it is appropriate to step back and ask what are the alternative plausible scenarios for stock mixing that should be considered? Are the diffusion and overlap models the only plausible alternatives that should be considered? This is a question beyond the scope of this paper but needs serious attention and can be answered only after all relevant data to date have been assembled and examined. However, from those gone over in this paper, it appears that the general overlap and diffusion models together with their estimated transfer coefficients cover a wide range of stock mixing possibilities. Once the plausible alternative models are put on the table, the question about model selection remains. As mentioned above, it is desirable to evaluate the plausibility of the alternative models or scenarios against all evidence available. Thus, not only the goodness of fit of the models to the data should be considered but other important evidence such as data from new genetic and age at maturity studies should also be used to evaluate the plausibility of the alternative models. The diffusion model has been acknowledged to be less plausible than the overlap model (ICCAT 1995; Cooke and Lankester 1996). The difference in estimated first ages at maturity between eastern and western spawners also casts doubt on the diffusion model which implies a single panmictic breeding population. The relative abundance data are also less consistent with the model as indicated above. Although the conventional tagging data are more consistent with the diffusion model (Porch et al. 2001), these data are quite fragmented. There are relatively few observations for larger fish, and tag reporting rates appear to have been decreasing over the last decade. Furthermore, the diffusion and overlap models have not yet been fitted to the growing database on archival and pop-up tags. Although these analyses have yet to be done, when all other evidence is taken into account, the overlap model still appears more plausible than diffusion (see Table 2). However, there are insufficient data yet to allow ruling out the diffusion model. The various possible mixing models have different implications for management. One possibility is that the fish spawning in the Gulf of Mexico are a genetically distinct population from the fish spawning in the Mediterranean, but that both populations feed on the eastern and western Atlantic fishing grounds. This scenario is consistent with the overlap model, but not the diffusion model. In this case, it would be necessary to estimate the fraction of each population present in each fishing ground, so that the quotas could be set at a level that would allow both populations to recover. More specific information about the seasonal and spatial distribution of each stock would be required to allow the more productive stock to be harvested without overfishing the less productive stock. Conversely, under the diffusion model, the stocks are panmictic, and the total quota should be low enough to allow the entire stock to rebuild but also to prevent depletion of the abundance of spawners on both the eastern and western spawning grounds. This latter point is important because a depletion of spawner abundance on one of the two spawning grounds could put the entire stock more at risk, especially if spawning conditions on the remaining ground deteriorated either temporarily or permanently because of changes in environmental conditions. Additionally a depletion of spawner abundance on one of the spawning grounds, e.g., the Gulf of Mexico, could lead to increased local scarcities of adults for harvesting since it is known that the many bluefin tuna exhibit extended periods of residency in particular parts of the North Atlantic (Block et al. 2001). SUGGESTED ASSESSMENT PROTOCOL A stock assessment approach that would account for the uncertainty in mixing and provide management advice based on the best available data could incorporate the following. (1) Identify a limited set of plausible alternative mixing models that represent alternative hypotheses on cross-oceanic migration and spawning site fidelity, say no more than two to four models. This would include the overlap and diffusion models but could also include a few more, depending on the most recently obtained data and their implications.

(2) Identify all relevant types of data available that could be used to evaluate the plausibility of the alternative mixing models. Sort the data into those to which the mixing models can be fitted such as tagging data (i.e., the conventional mark-recapture, pop-up tagging and archival tagging data), catch-at-age data, and relative abundance indices, and those to which the models cannot be fitted such as data on the first age of maturity for the eastern and western populations and genetic differentiation. (3) Formulate quantitative weightings for each alternative model based on the data to which the models cannot be fitted (Butterworth et al. 1996). If data are strong enough, e.g., on first age at maturity and genetic differentiation, this could allow the exclusion of one or more of the alternative models/hypotheses on stock mixing. Table 2 shows an example using the data in Table 1 to evaluate four possible movement hypotheses. The weightings listed are intended only for exemplary purposes. To use this method in an assessment it would be necessary to convene a meeting of the appropriate experts and agree upon the implications and relative importance of the various pieces of information. (4) Fit each of the stock mixing models to the available data and assess the weight of these data in support of each model. This can be done rigorously using Bayes' factors (Kass and Raftery 1995; McAllister and Kirchner 2001). For each alternative mixing model, multiply these Bayes' factors with the quantitative weightings in step 3 to provide the overall weighting for each alternative model. Note that this requires a model to which both catch data and tagging data can be fitted, so that it would require a statistical catch at age model instead rather than a VPA (also see recommendations of ICCAT 2001). (5) Evaluate stock status and recent trends in abundance using the few models that remain credible (no more than two or three different models that give the largest extremes in results). (6) Using each alternative model, evaluate the potential biological consequences of the alternative TAC options. Options would include a total TAC and how the TAC would be divided between east and west. (7) Present the results on stock status and policy outcomes showing the overall weights assigned to each of the alternative mixing models. One way to present results are to show the values of some index of policy performance, such as the probability that both stocks will rebuild to the biomass level that would support MSY by the year 2018, as shown in the example decision table (Table 3). The averaging of results across scenarios when uncertainty is large and only a few scenarios (e.g., only two extremes) are included should be avoided. This is because in theory only one of the scenarios can be correct. The average across scenarios with very different projections is far less likely. The suggested protocol still leaves out many important stock assessment issues. Even when a single mechanism for mixing is considered, there remains the issue of choosing the appropriate spatial units to model. Up until now only two-area models based on the east and west Atlantic have been considered (Butterworth and Punt 1993; Cooke and Lankester 1996; Porch et al. 2001). If the spatial resolution in the data allowed, a model with higher spatial resolution should be considered. One possibility would be to develop a model with different spatial areas based on the degree of overlap and the location of feeding and spawning grounds. For example, if an overlap model was to be considered, a more detailed model could include the following areas: (1) the Mediterranean Sea, (2) the known spawning region in the Gulf of Mexico, (3) a northwestern Atlantic feeding zone where the most overlap is understood to occur between eastern and western spawners,

(4) a middle north Atlantic feeding zone where less overlap is understood to occur between eastern and western spawners, (5) an eastern Atlantic feeding zone inhabited mainly by eastern spawners, and (6) a western Atlantic feeding zone inhabited mainly by western spawners. Other possibilities could include (a) combining proposed zones 3 and 4 to make it a 5 zone model and (b) combining zone 1 with zone 5, zone 2 with zone 6 and zone 3 with zone 4 to make a 3 zone model. The number and boundaries of the zones to include in a stock assessment should be determined by inspection of the available tagging data and what they suggest about zones of overlap and non-overlap. The zones should also be defined such that the tagging data available could provide estimates of the transfer coefficients for each stock between adjacent pairs of adjacent zones. Once the number and boundaries of the zones to include in the stock assessment procedure have been agreed, the same set of areas could be modeled in a diffusion model and an overlap model. The inclusion of a number of separate areas in a stock assessment model could permit the modeled area-, and age-specific abundance to be fitted to indices of relative abundance that corresponded to the same age group and area. The spatial zones within the model could also form the basis of new management units, each managed with its own management measures on a long-term basis (closed areas, gear restrictions) and annual basis (e.g., TAC). This model could then be used in policy projections to provide more precise area-specific assessment of stock status (whether for a one stock or two-stock assumption) and more precise area-specific policy advice. Also important in the formulation of a stock assessment approach, once the general types of models to be included have been decided upon, is the issue of model formulation and parameterization. The incorporation of tagging data in a stock assessment opens up huge numbers of possibilities for model parameterization. For example, Porch et al. (2001) freed up many mixing model parameters allowing, for example, for movement rates to vary with age, zone and year, firstyear post release effects on dispersal rates, and a tagger effect on recapture rates. A large number of model fitting scenarios were evaluated and the AIC criterion was used for model selection. However, as pointed out earlier, a variety of other model selection criteria could also be applied and might not necessarily give the same model choices. The issue of how to weight the tagging data versus the relative abundance indices also needs to be resolved. Objective model selection criteria and model fit diagnostics such as AIC, Bayes' factors and model deviance need to be considered to help sensibly determine model parameterization and to help minimize conflicts among contributing scientists regarding this (e.g., see McAllister et al. 2001). Uncertainty regarding the stock structure and movement is only one of the sources of uncertainty in the assessment of Atlantic bluefin tuna; others include the relationship between spawning stock biomass and future recruitment, and the effect of environmental factors on recruitment (ICCAT 2001). The various forms of uncertainty can be examined hierarchically (i.e., the uncertainty in recruitment estimation is only relevant after a functional form of the stock recruit relationship has been chosen). The decision table presented to the managers should only include a few scenarios that cover the range of the variation covered by the various dimensions of uncertainty. One additional consideration in the choice of a stock assessment modeling approach is the potential for bias in model projections as a result of the stock assessment modeling approach adopted. Recent retrospective analyses of several different VPA assessments have demonstrated that VPAbased projections have a strong tendency to be positively biased and to underestimate uncertainty (Patterson et al. 2000; ICCAT 2001). The use of ADAPT VPA methodology to produce stock projections under alternative TACs for north Atlantic bluefin tuna and the highly optimistic projections in the 2000 assessment of the western stock give reason for concern. It is recommended that retrospective analyses of the ADAPT VPA for this stock be conducted to check for such positive bias and that other statistically rigorous stock assessment methodologies such as statistical catch-atage analysis be run in conjunction with ADAPT VPA to evaluate the reliability of ADAPT VPA projections for north Atlantic bluefin tuna.

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Table 1. Information value of data collected. GOM refers to Gulf of Mexico. Med refers to Mediterranean. I# refers to potential inconsistencies with other data. Data type and reference

Observed

Strengths (S)/Limitations

Implications for mixing hypotheses

Conventional tags (I1) -described in Porch et al. (2001)

data analysis indicates 1-3% oceanic crossing rates, i.e., over 45oW from both east and west

- 0 crossing hypothesis is ruled out - some mixing across 45oW occurs

Pop-up tagging of large tunas in GOM Block et al. (2000)

-fish from GOM have not been observed to cross 45oW

- large sample size (S) - mostly smaller fish tagged -reporting rates decreasing - fewer tags released in east - very few fish tagged - high recovery rate of tags and information about fish (S)

Pop-up tags and archival tagging of NW Atlantic Tuna (I1) Block et al. (2000, 2001) Lutcavage and Luckhurst (2001) Pop-up tagging of Med fish De Metro et al. (2001) Archival tagging in AdriaticYamashita and Miyabe (2001) Genetic Studies - Ely et al. (2001)

- 30-58% of fish tagged cross 45o W - some fish visited Med. others visited GOM spawning zones

- relatively few large fish tagged

- Several fish mig. out of Med but no further than 30oW -archival tagged fish all recovered in Med. - no difference between NW Atlantic and Med fish found in large sample sizes of 127cm –277cm fish - no difference between GOM and Med larval fish -preliminary data show 67-89% correct classification of Pacific vs Med. fish - GOM first size at maturity is much larger than that in Med fish - growth rates higher in GOM

- few recoveries (12 fish) - pop – ups after < 250 d

Otolith micro-constituents -ICCAT (2001c) Size and Maturity at Age - Block et al. (2000, 2001) - Susca et al. (2001)

CPUE data -Porch et al (2001) Spawning location and timing -NRC (1994)

-CPUE data alone is consistent with some East to West movement - separate spawning areas in GOM, Med, central Atlantic? -spawning in Spring in GOM, summer in Med.

- lack of difference found does not indicate a single stock

-distinguishes region of residence, not origin - sample size of large fish is low

- can't rule out spawning site fidelity hypothesis for GOM spawners

- potentially high rate of crossing of 45oW - potentially large catches of eastern spawners from west and vice versa. - can't rule out eastern spawners feeding in Northwest Atlantic - can't rule out spawning site fidelity of Med spawners - Med fish have eastern Atlantic home range. - Equivocal results

-Results preliminary - suggests different biotypes, i.e., phenotypes but not necessary different genotypes - suggests some site fidelity of fishes but does not rule out some mixing of spawners across spawning grounds

Suggestions for further investigation - tag more larger fish - tag more fish in the east Atlantic

- tag more large fish in GOM and Med. at spawning time and set tags to pop up at 1 yr and then 2 years. - tag more larger fish and with pop up tags – have longer lags in time to tag release

- apply longer pop-up periods -increase sample size of archival tags - try to find other genetic identifiers of tuna stock - test for differences only in larval and spawning fish from the GOM and Med. -Develop large samples, including fish from GOM and Med.

Table 2. An illustration of some relative weightings of information that could be used to develop prior probabilities for the alternative scenarios on stock mixing. "Odds" values are assigned zero for inconsistency between the model and the data, 0.5 for low support, 1 for ambiguity and 2 if the data supports the model. The CPUE and conventional tagging data are not included because they can be fit within the stock assessment model. The data sources are weighted by their relative information content with respect to mixing hypotheses, and the odds are multiplied across data sources before normalization. Sources of information Normalized Pop-up, archival Size and maturity Spawning site Genetic studies Otolith microand conventional Product at age location and constituents (not tags1 timing done yet) Weight of data 0.1 0.1 0.2 0.1 0.5 source Hypothesis No mixing 1 1 2 2 0 0.0 Diffusion 2 1 1 1 1 0.30 Overlap 1 1 2 2 1 0.62 Single wellmixed population 2 1 0.5 0.5 1 0.08 1 Note that the tagging data should not be used in this particular analysis if the result, the final column were to be used as a prior for stock assessment analyses of tagging, catch rate and catch at age data that were to compare alternative mixing models. Table 3. Example decision table for bluefin tuna mixing models. The index of quota policy performance would be something like the probability of rebuilding both stocks to Bmsy by the year 2018. The quota policies would include quotas for both the east and the west stocks. The probabilities of each model would be calculated as described in step 4 of the text. Note that the final column should not be used in decision analysis because the average of results from two different stock assessments is often far less likely than the result under each model. Alternative mixing models Expected value of index across models Model 1Prob Model 2 Quotas (model 1) Prob(model 2) Quota policy 1 Index(1,1) Index(1,2) Index(1,1)*Prob(1) +Index(1,2)*Prob(2) Quota policy 2 Index(2,1) Index(2,2) Index(2,1)*Prob(1) +Index(2,2)*Prob(2) Quota policy 3 Index(3,1) Index(3,2) Index(3,1)*Prob(1) +Index(3,2)*Prob(2) etc.