Modeling Approach

The Multistock Age-Structured Tag-integrated assessment model (MAST) is a mixed-stock, seasonal, and spatially explicit statistical catch-at-age model that can be fitted to relative abundance indices, age proportions, and otolith microchemistry, as well as to conventional and electronic mark-recapture data. The model was written and fitted to data using the software AD Model Builder, which is freely available from www.admb-project.org (ADMB Project 2009). The model and statistical fitting procedure are described in detail in the online Text S1. We characterized parameter uncertainty using Markov Chain Monte Carlo simulation.

The MAST model consists of four major components:

1. Initialization of the model based on steady-state conditions (unfished numbers and biomass) given the model's parameters;
2. Updating the state variables (numbers and biomass at age in each area);
3. Relating the state variables to observations on relative abundance, age-composition information, and mark-recapture observations; and
4. Evaluating the probability of model parameters given the data.

We provide a description of each model component in the main text, and refer readers to the Model Description in the online Text S1 for further detail.

We defined five geographic areas for quantifying movement dynamics: the Gulf of Mexico, which we assume is the western-stock spawning area; the Gulf of St. Lawrence, which we assume contains primarily western-stock fish [11]; the western and eastern Atlantic Ocean, which we assume to be mixed-stock areas; and the Mediterranean Sea, which we assume is the eastern-stock spawning area. We used these areas because they are either mixed-stock areas in the eastern and western Atlantic Ocean basins that have historical importance at ICCAT, or because they appear to be nearly exclusively western-stock (the Gulf of Mexico and Gulf of St. Lawrence) or eastern-stock (Mediterranean Sea) areas. Figure S1 shows the model areas and the electronic tag geoposition data. By including the Gulf of St. Lawrence as a distinct area, additional tagging data and an additional CPUE abundance index can be used in modeling the population dynamics of the western stock [11]. MAST models western-stock fish as moving between the Gulf of Mexico, the Gulf of St. Lawrence, and the western and eastern Atlantic (corresponding to area indices 1–4). MAST models eastern-stock fish as moving between the Mediterranean Sea and the eastern and western Atlantic (area indices 3–5).

We parameterized movement matrices using gravity models for the model-fitting base-case. The probability of fish moving from one area to another is defined in terms of a movement matrix µ. Each movement matrix consists of rows representing area of origin and columns representing the destination area. Each row element of µ therefore represents the probability of fish moving from area j (rows) to area j' (columns); each row represents a probability vector υ, where υ = (υ₁, υ₂, …, υ_n) and Συ = 1. Here we estimated a single propensity of fish to stay in a given area—that is, “gravity” (the diagonal elements of µ)—which is assumed to capture the attractiveness of that area relative to the areas associated with the off-diagonal elements. These latter elements are given as (1-µ_j,j)/(n–1), where n is the number of stock areas for stock i. An alternative to the gravity model is the bulk-transfer model, in which the full matrix of movement probabilities is estimated. Some biological detail is lost in using this gravity parameterization; the main advantage is that it substantially reduces the number of estimated parameters compared with the bulk-transfer case. We discuss the bulk-transfer parameterization and the sensitivity of the model in the online Text S1.

For Atlantic bluefin tuna, there is strong seasonal and ontogenetic dependence of movement rates, where fish of different ages use different habitats during the year for foraging or spawning [6], [7], [18]. To account for these phenomena, we modeled quarterly time-steps and two age-groups: 0–7 and 8+ We assumed that movement transitions to spawning areas (the Gulf of Mexico for the western stock, and the Mediterranean Sea for the eastern stock) during the spawning quarter were given by the maturity-at-age schedule.

The MAST model uses the management-oriented approach [28], meaning that the model is initialized using maximum sustainable yield (MSY) and the fishing rate that produces maximum sustainable yield (F_msy). Under this formulation, MSY and F_msy are the leading estimated parameters. Then, using estimated gear selectivity as well as input growth [1], mortality, and maturity parameters, we derived the recruitment compensation parameter κ [29], initial numbers, and initial biomass B₀. Maturity-at-age schedules were based on [30] for the western stock and [31] for the eastern stock. The model was parameterized with initial numbers-at-age in the spawning area and then run for 25 years to allow the model to equilibrate between areas (see Tables S1–S7).

Initial numbers-at-age for each stock (see Tables S1–S7) were updated in each time-step (i.e., the next quarter) according to natural and fishing mortality, as well as migration parameters. Age-zero recruits were predicted by a Beverton-Holt stock recruit function (Eq. 25, Table S5). Details of the state dynamics are described in the online Text S1.

Parameter Estimation

We estimated the parameters that define the model by fitting predicted observations (component 3) to observed data. The modeling procedure starts with initial parameter values (see Tables S1–S5) that define the state variables, then proceeds through the state dynamics (Tables S4 and S5), where state variables such as numbers-at-age for each stock are updated at each time-step. Ultimately, the model calculates the statistical objective function value, which represents the probability of the model given the data (Table S6). Parameters are estimated using a conventional nonlinear optimization procedure. AD Model Builder was used to implement the model.

For all data types except electronic tag data, we used conventional statistical likelihoods. We fitted relative abundance indices using Walters and Ludwig's [32] formulation (see Tables S5 and S6). We fitted otolith microchemistry using binomial likelihoods, and conventional mark-recapture data using negative binomial likelihoods (Tables S4 and S5). If the stock-of-origin for a given cohort was known through a cohort's area of visitation or marking, then that cohort's survival and movement dynamics were modeled according to the movement probability matrix for that stock. However, for 85% of cohorts (Table S10), stock of origin was unknown. In these cases, the likelihood was computed twice; that is, using movement probability matrices from western and eastern stocks (Eq. 1.38, Table S5), with likelihood weights given by the ratio of vulnerable numbers of stock i to total vulnerable numbers in that area at that time.

For electronic tag data, we used discrete, state-space likelihoods. We modeled the state of tags through discrete states at each model time-step [33] (see Eqs. 1 and 2 in Table S2). We assumed that the tag was attached to a live fish in area j; captured on a fishing vessel; attached to a fish that died of natural causes; or shed from the fish (Table S8). For electronic tags, equations describing state transitions are listed in Table S8, and parameters for electronic tag observation probabilities p(y_t|s_t) are given in Table S9. When modeling tag tracks, capture probabilities represent the probability of obtaining a geoposition for a particular tag type. In the case of pop-up satellite archival tags, there are complete tag tracks (i.e., spatial positions at each quarter), so these observation probabilities are 1. For archival tags, however, not all tag tracks are complete; there can be missing geolocations at times between the last geolocation recorded by the tag and the location given by the vessel position at time of recapture. In these cases, we estimated a single observation probability parameter for archival tags (Table S9) that represents the proportion of time between the release of the tag and its recovery in which it was possible to determine the geoposition of the tag.

Data

We used catch data from the 2010 ICCAT CATDIS database (www.iccat.int). CATDIS is the official database that contains catches in 5×5 degree grid squares, by quarter and gear. We separated catches into four gear categories: longline, purse seine, bait boat, and other. For each catch record, an area was assigned according to Fig. S1. The input data for MAST consisted of total catches by fleet, area, and quarter from 1950 to 2008 (Fig. S2). To account for large catch underreporting from 1998 to 2007 in the Mediterranean Sea, we inflated catches reported in the Mediterranean. We used the same procedure as RUN 14 of the 2008 ICCAT stock assessment, where total eastern catches were assumed to be 50,000 metric tonnes (mt) from 1998 to 2006 and 60,000 mt in 2007 [13]. At the time of writing, catch data for 2008 and 2009 were not yet available, so we assumed that the total eastern and western catches in these years were the recommended quotas. This may be a reasonable assumption, since there is evidence that compliance has improved considerably with ICCAT's introduction of a vessel monitoring system in 2008 [13].

We aggregated conventional tag data into cohorts (h) for fish that had the same assigned age and were captured in the same quarter; these data are available in ICCAT's conventional tag database (www.iccat.int) and are summarized in [5]. (We used the version of the database updated in September 2009.) The data were filtered to remove incomplete records that were missing size or location data at either release or recapture. The filtered conventional tag data set consisted of 47,439 releases that were distilled into 1732 cohorts. Of these, 125 tag cohorts were assigned to the western stock and 142 to the eastern stock, and 1465 were unknown (Table S10). Details of how tagged fish (both electronic and conventional) were assigned to stocks and age-groups can be found in the online Text S1.

Between 1996 and 2008, a total of 968 bluefin tuna were electronically tagged with internally implanted archival tags and/or externally attached pop-up satellite archival tags at tagging locations along the U.S. East Coast, in the Gulf of Mexico, in the Gulf of St. Lawrence, off Ireland, and in the Mediterranean Sea [6], [7], [18]. The daily geopositions of electronic tags were aggregated to quarterly area assignments. If a tag was reported being in more than one discrete stock area, it was assigned to the area where it spent the greatest proportion of time. Additional details of how satellite geopositions were determined are given in the online Text S1.

We used the commercial CPUE time-series and catch-at-age proportions from the ICCAT assessment document [13]. We used the catch-at-age data from the assessment to define catch-at-age proportions [13] from age 1 to 10+in the western Atlantic (areas 1–3) and eastern Atlantic (areas 4–5), which were based on western and eastern catch-at-age data from 1960–2007 and 1970–2007, respectively. Table S11 is a summary of which CPUE series we used, as well as the corresponding quarters and area for each.

We extracted otolith microchemistry stock-composition data from Rooker et al. [11], who divided their data into three age-groups: giant (age 10+), medium (age 5–9), and school (age 4 or younger). They had stock-composition samples for the Mediterranean, Gulf of Mexico, Gulf of St. Lawrence, Gulf of Maine, and the Mid-Atlantic Bight. We fitted the model (see below) to stock-composition ratios from the Gulf of Maine and the Mid-Atlantic Bight only because it was assumed that the Gulf of Mexico and Gulf of St. Lawrence areas were 100% western stock and the Mediterranean was 100% eastern stock. The stock-composition data used in the model are summarized in Table S12.

Uncertainty and Projections

We computed marginal posterior probability distributions for all estimated parameters using MCMC simulation with six chains. One value was sampled for every ten iterations, and we ran the MCMC until the multivariate posterior scale reduction factor [34] was below 1.05. We present fishing mortality rate reconstructions by area and gear type at the posterior mode; posterior samples of western and eastern bluefin tuna spawning stock biomasses; stock status relative to maximum sustainable yield; and stock composition in mixed-stock areas.

We ran the base-case model with a series of management options, including complete fisheries closures, spatial closures, and other quota options. We chose scenarios to reflect a broad range of possibilities in Atlantic bluefin tuna management. The first scenario (i) represents total closures, which might have occurred with listing under CITES. For the quota scenarios, we assumed future bluefin tuna catches west (W) and east (E) of the 45° meridian from 2010 to 2025 to be: (ii) 1750 mt W/12,900 mt E, with no Gulf of Mexico closure; (iii) 1750 mt W/12,900 mt E, assuming a Gulf of Mexico closure with catches redistributed to the western Atlantic; (iv) if eastern catches continued to be double the current quotas, that is, 1750 mt W/25,800 mt E; and (v) an eastern overfishing case of 1750 mt W/60,000 mt E. This final scenario was intended to capture what might have occurred if Atlantic bluefin tuna catches continued at 2007 levels.

In addition to parameter uncertainty, we examined the sensitivity of the base-case results to a suite of alternative model parameterizations and reporting-rate-prior distributions. The details of each sensitivity case and the corresponding effect of each to key stock status metrics are listed in Table S13, and the effect on conventional tag reporting rates is given in Table S14.

Historical Abundance and Exploitation of Atlantic Bluefin Tuna

MAST estimates the initial stock size (B₀) of the western population to be 100–120 kt, and that of the eastern stock to be 800–900 kt (Figs. 1A and B). The ranges reflect the most credible interquartile ranges. The estimates of the maximum sustainable yield (MSY) from which these initial biomasses were calculated are 3.9 and 25 kt for the western and eastern stocks, respectively. Predictions of stock depletion rates relative to 1950 are 17% for the western stock and 33% for the eastern stock.

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Figure 1. Box plots of posterior samples of the spawning stock biomass (kt) of (A) western and (B) eastern Atlantic bluefin tuna.

The horizontal lines within the blue bars represent the posterior median values, the blue bars represent the interquartile values, and whiskers are 1.5 times the interquartile range. The dashed horizontal lines represent the spawning stock biomass that would produce maximum sustainable yield.

https://doi.org/10.1371/journal.pone.0027693.g001

Furthermore, MAST indicates that the western bluefin tuna stock was subject to overfishing and was depleted to below the MSY stock biomass level (B_msy) relatively early in the fishery. Longline and purse-seine fishing in the Northwest Atlantic in the 1960s depleted the stock to levels below MSY before 1970 (Fig. 1A). The large annual Gulf of Mexico longline catches (approximately 3–4 kt) that occurred in the 1970s corresponded with high fishing mortality rates (Fig. 2B) on western-stock spawners, which further depleted the stock.

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Figure 2. Mean annual fishing mortality rates (yr^-1) for Atlantic bluefin tuna by longline (LL), purse-seine (PS), bait boat (BB), and other (Oth) gear types in (A) the Gulf of Mexico, (B) the Gulf of St. Lawrence, (C) the western Atlantic Ocean, (D) the eastern Atlantic Ocean, and (E) the Mediterranean Sea.

Red and green dotted lines represent F_msy for western and eastern stocks, respectively.

https://doi.org/10.1371/journal.pone.0027693.g002

Observed declines in western Atlantic biomass have also been the result of a declining eastern population. The model predicts that the decline of the eastern stock to below B_msy has occurred as recently as the last 10 years (Fig. 1B), owing largely to substantial illegal and unreported catches in the east [13]. Concurrent with the depletion of eastern populations over the last 15 years, the model predicts a steady increase in the ratio of western to eastern fish in the western Atlantic Ocean (Fig. 3A).

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Figure 3. Predicted ratio of the numbers of western Atlantic bluefin tuna to total numbers of tuna from 1950 to 2008 in the (A) western Atlantic Ocean and (B) eastern Atlantic Ocean during the first quarter (black), second quarter (red), third quarter (green), and fourth quarter (blue).

https://doi.org/10.1371/journal.pone.0027693.g003

The model points to serial, regional depletions as fishing effort has shifted spatially over time. Japanese longlining catches in the Gulf of Mexico in the 1970s were relatively small, but concentrated on a smaller number of western-stock spawners (Fig. 2A). In the western Atlantic, high fishing mortality rates occurred initially from longlining and purse seining, which removed as much as 20,000 mt annually in the 1960s off the coastal United States (Fig. 2A). The Norwegian purse-seine fisheries caught approximately 20,000 mt annually in the early 1960s, exerting mean fishing mortalities of up to 0.8 yr⁻¹ until this fishery rapidly collapsed in 1963 [24]. These early fisheries occurred in mixed-stock areas of the western and eastern Atlantic, and the model predicts that a small proportion of Nordic purse-seine catch (Fig. 2D) could have consisted of up to 10% western stock (Fig. 3B). However, the eastern-stock subsidy of western Atlantic bluefin tuna fisheries was substantial, with the western-stock ratio ranging between 50% and 90% western and 10–50% eastern during that period (Fig. 3A). Fishing mortality rates were well above the MSY rate (F_msy) for both stocks in all mixed-stock areas (Figs. 2C and D).

Relative to 1950–1970, eastern Atlantic bluefin tuna catches fell in the 1980s, but then increased again in the 1990s. Since 1990, the bulk of the tuna fishing effort has moved into the Mediterranean Sea in association with purse seining to populate tuna ranches. During this period, the largest Atlantic bluefin tuna catches in history occurred between 1998 and 2007, with maximum catches of approximately 60 kt occurring in 2007 in the eastern Atlantic and Mediterranean Sea [13]. With catches of this magnitude, the model suggests that a very large number of eastern-stock fish, up to 800–900 kt, must have existed in the Mediterranean Sea to have supported such removals. Fishing mortality rates were approximately double F_msy between 1995 and 2008 (Fig. 2E).

Future Projections of the Atlantic Bluefin Tuna Fishery

MAST predicts that western Atlantic bluefin tuna stock rebuilding depends on eastern Atlantic and Mediterranean catches. If oceanwide catches are zero (scenario i), the model predicts that the western stock has a low probability of being at levels that produce maximum sustainable yield (median B₂₀₂₀/B_msy = 0.81, Fig. 4A), but that eastern-stock rebuilding will be much faster (median B₂₀₂₀/B_msy = 1.4, Fig. 4B). MAST also predicts that relative to no closure (scenario ii, Figs. 4C and D), western-stock rebuilding will not be faster with a Gulf of Mexico closure (scenario iii, Figs. 4E and F), and eastern-stock rebuilding will be unaffected. However, if eastern-stock rebuilding is slow, or if the stock declines, then western-stock growth must also be slow, or decline, without western quota adjustments to compensate for the loss in the eastern subsidy. In addition, MAST predicts western- and eastern-stock median B₂₀₂₀/B_msy ratios to be 0.51 and 0.92, respectively, for the double eastern quota (scenario iv, Fig. 4G and H), and 0.36 and 0.35, respectively, for the historical overfishing case (scenario v, Fig. 4I and J). In all cases, the high variability of predicted spawning stock biomasses during the recovery may prevent the benefits of reduced fishing quotas from being statistically detectable for many years.

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Figure 4. Box plots of the predicted ratio of biomass to the biomass that would produce maximum sustainable yield (B_t/B_MSY) under alternative management quotas for western (left column) and eastern (right column) Atlantic bluefin tuna stocks under various scenarios: total fisheries closures (A and B); catches at 1750 mt West and 12,900 mt East, with a Gulf of Mexico closure (C and D); catches at 1750 mt West and 12,900 mt East, with no Gulf of Mexico closure (E and F); catches at 1750 mt West and 25,800 mt East (G and H); and catches at 1750 mt West and 60,000 mt East (I and J).

The horizontal lines within the blue bars represent the posterior median values, the blue bars represent the interquartile values, and whiskers are 1.5 times the interquartile range.

https://doi.org/10.1371/journal.pone.0027693.g004

The redistribution of quota is likely to limit the effectiveness of large-scale closures. Under the Gulf of Mexico closure scenario (iii), the quota tonnage associated with the bycatch and dead or discarded bluefin in the Gulf is redistributed to the western Atlantic. It follows that the predicted landings there would include larger numbers of immature fish of both western and eastern stocks to compensate for their smaller size. The redistribution of quota would not require the Gulf of Mexico fleet to move to western Atlantic fishing areas, because unused quotas could simply be reallocated to other sectors (such as rod and reel) or even other countries through reallocations at ICCAT. There is additional uncertainty over the effects of a Gulf of Mexico closure, because bycatch and dead discard estimates for both inside and outside the Gulf of Mexico are unknown.