4
Fish Stock Assessment

In this chapter, the committee reviews the principal components of the assessment of Atlantic bluefin tuna and performs a reanalysis based on its review and the significant rates of transfer across the Atlantic Ocean presented in Chapter Three. Three major components of assessment are growth, catch per unit effort (CPUE) indices, and virtual population analyses (VPA). In the section for each component, the nature of the review and of the reanalysis performed is described.

GROWTH

It was beyond the committee's purview to undertake a detailed examination of growth. Developments in the analysis of growth curves include the generalization of many models of sigmoid growth into a single function (Richards, 1959; Fletcher, 1975; Schnute, 1981). The Richards (or Schnute case 1) growth model has four parameters and contains many three-parameter growth models as special cases (e.g., von Bertalanffy, Gompertz, logistic). The technique of nonlinear least-squares regression is frequently used to estimate parameters.

Environmental and/or genetic factors may affect the shape parameter of the growth models for Atlantic bluefin tuna (in particular, in the Mediterranean Sea versus the Gulf of Mexico). The shape parameter may be an important aspect of growth that is sensitive to environmental conditions or genetic differences which is most readily adjusted by the organism during early life history. Thus, careful comparisons of this shape parameter may be useful for a better understanding of the selective contributions of the two spawning areas.



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An Assessment of Atlantic Bluefin Tuna 4 Fish Stock Assessment In this chapter, the committee reviews the principal components of the assessment of Atlantic bluefin tuna and performs a reanalysis based on its review and the significant rates of transfer across the Atlantic Ocean presented in Chapter Three. Three major components of assessment are growth, catch per unit effort (CPUE) indices, and virtual population analyses (VPA). In the section for each component, the nature of the review and of the reanalysis performed is described. GROWTH It was beyond the committee's purview to undertake a detailed examination of growth. Developments in the analysis of growth curves include the generalization of many models of sigmoid growth into a single function (Richards, 1959; Fletcher, 1975; Schnute, 1981). The Richards (or Schnute case 1) growth model has four parameters and contains many three-parameter growth models as special cases (e.g., von Bertalanffy, Gompertz, logistic). The technique of nonlinear least-squares regression is frequently used to estimate parameters. Environmental and/or genetic factors may affect the shape parameter of the growth models for Atlantic bluefin tuna (in particular, in the Mediterranean Sea versus the Gulf of Mexico). The shape parameter may be an important aspect of growth that is sensitive to environmental conditions or genetic differences which is most readily adjusted by the organism during early life history. Thus, careful comparisons of this shape parameter may be useful for a better understanding of the selective contributions of the two spawning areas.

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An Assessment of Atlantic Bluefin Tuna STANDARDIZATION OF WESTERN ATLANTIC BLUEFIN TUNA CATCH RATES (CPUES) Introduction Several indices based on catch rate as measured by CPUE are used in the VPA of Atlantic bluefin tuna, as described in the International Commission for the Conservation of Atlantic Tunas (ICCAT) report (ICCAT, 1993; table 3 gives the annual values). These indices are of critical importance because their trends are influential in determining the final trend in population parameters from the analysis. The committee wanted to evaluate the uncertainty in these indices and therefore obtained data from three indices, as explained below. The methods used to obtain the indices were examined and as a consequence, the committee performed analyses to reestimate annual values for the indices. In addition, hypothesis of trends in the CPUE data and abundance indices were made, using a robust procedure described below. This trend analysis was performed on the new information as well as the abundance indices from Table 3 of the ICCAT report. Model Development The use of CPUE as an index of abundance relies on the direct relationship CPUE = C/E = qN, where C is catch, E is effort, q is the catchability coefficient, and N is abundance, biomass, or density. A common problem has been that the value of q may depend on various fishing methods, gear types, and environmental conditions. When annual indices of abundance are desired, the annual trend in CPUEs will reflect the abundance trend only if q is constant over years. However, because fishing techniques and environmental conditions may vary annually, CPUEs need to be standardized so that their trend is independent of these other factors. The annual trend in standardized CPUEs will reflect changes in CPUEs that are not attributable to the standardization factors. Therefore, the annual trend of the standardized CPUEs is attributable to factors not used in the standardization procedure, the most important of which is abundance. Nonlinear relationships between CPUE and abundance were not considered in this report owing to data limitations, but it is true that the presence of nonlinear relationships would induce additional uncertainty about population status and should be considered further. One popular technique for standardizing catch rates is the use of general linear models. Usually, the CPUEs are transformed so that the annual effects and standardization factors will be multiplicative; for example, (1)

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An Assessment of Atlantic Bluefin Tuna which is equivalent to the additive model (2) where A represents annual effects, V represents effects of the fishing operations, X represents environmental effects, ε represents random error term with mean zero and variance σ 2, and Z represents additional effects on catchability. A serious problem arises when observations of zero CPUEs, whose logarithms are undefined, appear in the data. The usual solution to this problem is to add a constant: (3) Model 3 is equivalent to multiplicative model 1 with the addition of the constant c. For small values of c relative to the magnitude of the CPUE data, the two models have similar structures. However, if the constant is large, the structure of model 3 could be much different from that of model 1. No longer is CPUE directly proportional to abundance in model 3. Thus, the major problem with using a large constant is that the potential exists for altering the basic multiplicative structure of the model. Indeed, the constant induces a structural change in the form of the model and may create interactions and significant effects among other factors, which would not exist without the constant (or with a small constant) and vice versa. The models for standardizing Atlantic bluefin tuna CPUEs have used constants such as 1 and 10 × max(CPUE) (Porch and Scott, 1993). The two resulting trends in standardized CPUEs differed. Furthermore, the transformed data did not meet the normality requirements assumed in testing the significance of the factors in the model, making inferences about the significance of the factors imprecise. There is little support in the statistical literature for choice of a large constant in relation to the magnitude of the data (Zar, 1974; Berry, 1987). In Berry's paper, the examples show small constants in relation to the magnitude of the data, except for one case where a large value was deleted to examine sensitivity. In this case the suggestion is made that the data may not need to be transformed at all, rather than having a large constant added to the observations. Berry's paper had the goal of minimizing skewness and kurtosis, but with Atlantic bluefin tuna the primary goal is to obtain a measure of abundance. These two goals may not be compatible. To resolve some of these problems, other methods have been investigated to standardize Atlantic bluefin tuna CPUEs (Porch and Scott, 1993), with emphasis on solving the problem of zeroes, including the Box-Cox transformation suggested by Berry (1987) and the delta-lognormal distribution (Lo et al., 1992). No matter what transformation is used, back-transformation to the original CPUE scale requires consideration of bias. In the lognormal case, estimating the

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An Assessment of Atlantic Bluefin Tuna predicted values as exp(mean(ln(CPUE))+ ) removes much of the bias. For the constant-added log transformation, see Porch and Scott (1993). Another complication that arises in standardizing CPUEs with general linear models is weighting. Some fishing trips are longer than others. Therefore, these trips sample more area and should be weighted more. In other words, ∑C/∑E is less variable than l/n(∑C/E), suggesting that effort weighting is desirable (see Quinn et al., 1982); that is: (4) The underlying model for catch in this situation is: (5) where ß is the CPUE parameter (qN), and ε is an error term with mean 0 and constant variance σ2. Note that this error structure is different from that in models 1 and 2. A recasting of model 5 as: (6) suggests that the variable C/ √ E is a candidate for further analysis. Thus, the standardization model 1 or 2 could be recast with the error structure of model 6: (7) where Θ is the set of unknown parameters {µ,{A},{V},{X}, …}. By using a least-squares criterion, parameters can be estimated by minimizing: (8) which shows that this is an effort-weighted nonlinear least-squares procedure. For this model, predicted CPUEs do not require any bias adjustment. Subsequent to the writing of the first draft of this report, the committee found a similar method that is available in the commercial software package S-Plus®.1 Application of the S-Plus® log-linear model with Poisson error assumption produces results similar to the ones given in this report. 1    Statsci, 1700 Westlake Ave. N., Suite 500, Seattle, WA 98109.

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An Assessment of Atlantic Bluefin Tuna Analyses The committee was able to obtain data for three indices: the rod and reel survey for small fish (ages 1 to 5), the rod and reel survey for giant fish (ages 8+), and captains' logbook data for giant fish. The committee reanalyzed these data as explained below.2 Rod and Reel Indices for Small Fish Catch rates of small bluefin tuna were standardized by the general linear model method of Brown and Browder (1993), except that the constant for the transformation, ln(CPUE+c), was set to approximately 0.3, which is 0.1 × mean CPUE. This value was small enough to maintain the character of the original data but large enough to prevent the indeterminacy at the origin, which occurs in the logarithm function. It was assumed that each combination of boat name and state of operation represents a unique boat. Although this is not entirely true because more than one boat may have the same name, the approximation is fair. Then, to test the assumption that the CPUE trend is affected by the experience of skippers, three data sets were made. The first data set included all boats. In the second, trips by boats for which no bluefin tuna had ever been sampled by the National Marine Fisheries Service were excluded. This restricted the sample to boats that had some experience catching bluefin tuna. The third data set had more restrictive rules: only boats for which bluefin tuna had been sampled in more than one year were used. No estimates were made prior to 1984 for data sets two and three, because boat names were not recorded before then. Also, 1984 data were excluded from the small bluefin tuna analysis because boat type data used for standardization were absent in 1984. Back-transformed, corrected, least-squares means (Brown and Browder, 1993) from the general linear models on all three data sets produced similar results, as shown in Table 4-1. The Standing Committee on Research and Statistics (SCRS) analyses originally showed a dramatic decline in 1992; however, after data processing errors were corrected by Inter-American Tropical Tuna Commission scientists under the committee's direction, the decline is much smaller. Effort weighting was attempted for this logarithm model to see if weighting altered the results. However, this weighting caused the method to produce unreliable results for some unknown reason. Because the choices of the weighting factor and the constant of transformation affect the estimated trend in standardized CPUE, we used the effort-weighted, nonlinear, least-squares regression model (model 7) of the form C/ √ E 2    The committee considered conducting bootstrap analysis, but didn't because of the time constraint and the problem of how to run this analysis without having all the raw data.

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An Assessment of Atlantic Bluefin Tuna TABLE 4-1   Estimates of small bluefin tuna CPUE (catch per 100 hours) from rod and reel and handline.* Year All Boats Trips Only Boats for Which Tuna Were Sampled Trips Only Boats for Which Tuna Were Sampled in Two or More Years Trips 80 56.1 720 N/A — N/A — 81 17.1 454 N/A — N/A — 82 143.1 308 N/A — N/A — 83 29.6 784 N/A — N/A — 84 N/A — N/A — N/A — 85 30.0 416 37.2 383 42.5 209 86 46.0 583 62.1 499 62.5 345 87 67.7 491 84.6 420 96.4 276 88 49.9 357 49.5 307 55.9 195 89 59.5 646 73.4 575 77.7 401 90 39.8 667 42.7 604 45.6 440 91 63.8 619 55.1 561 51.6 345 92 37.8 590 41.0 398 59.2 197 N/A = data not available. * The committee was unable to obtain confidence intervals due to time constraints. = √ E × exp(Y + B + A) + ε, where C is the catch, E is the effort, Y represents the annual effects, B represents the boat type effects, A represents the area effects, and ε, is the error. The results (Table 4-2 and Figure 4-1) were similar to those of the general linear models, suggesting no trend in abundance effects over time. Rod and Reel Indices for Giant Bluefin Tuna These data were analyzed in a similar fashion as the data for small fish. Both the back-transformed, corrected, least-squares means from the general linear model of ln (CPUE+0.05) and the effort-weighted nonlinear least-squares regression model were used. The significant factors used were area, fish targeted, and month. Fish targeted and area were combined into three categories, GOMA, STNH3 targeting giant bluefin tuna and STNH targeting marlin and other tunas. Because the second category was present only in 1983, the effect of category 2 on 1983 is removed. No annual trend was apparent after 1983 (Tables 4-3 and 4-4, Figure 4-2). The SCRS analyses showed a dramatic decline in 3    The acronyms GOMA and STNH stand for the Gulf of Maine area and the southern New England to New Jersey area, respectively (Cramer and Turner, 1993).

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An Assessment of Atlantic Bluefin Tuna TABLE 4-2 Relative abundance of small bluefin tuna from effort-weighted nonlinear least-squares regression (1992 = 1.00), including lower and upper 95% confidence limits.a Year All Boats Lower Upper Only Boats for Which Tuna Were Sampled Lower Upper Only Boats for Which Tuna Were Sampled in Two or More Years Lower Upper 80 1.93 1.80 2.08 N/A - - N/A - - 81 0.43 0.32 0.59 N/A - - N/A - - 82 2.12 1.94 2.32 N/A - - N/A - - 83 0.77 0.65 0.91 N/A - - N/A - - 84 N/A - - N/A - - N/A - - 85 0.80 0.62 1.03 0.87 0.67 1.13 0.76 0.55 1.06 86 1.04 0.87 1.24 1.12 0.93 1.33 0.79 0.62 1.00 87 1.63 1.41 1.88 1.85 1.60 2.13 1.43 1.20 1.70 88 1.05 0.83 1.32 1.08 0.86 1.37 0.84 0.63 1.12 89 1.55 1.37 1.74 1.67 1.48 1.87 1.24 1.07 1.43 90 0.78 0.63 0.95 0.80 0.65 0.99 0.55 0.42 0.73 91 1.84 1.67 2.04 1.89 1.70 2.10 1.64 1.46 1.86 92 1.00 0.83 1.21 1.00 0.80 1.24 1.00 0.78 1.28 N/A = data not available a Results from an earlier version of the method. Results from a later version differ slightly from the ones in this table but do not cause any changes to the conclusions of the report.

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An Assessment of Atlantic Bluefin Tuna FIGURE 4-1  Western Atlantic Ocean small bluefin tuna indices. 1992; however, after data processing errors were corrected by Inter-American Tropical Tuna Commission scientists under the committee's direction, no such decline could be detected. Captains' Logbook Data for Giant Bluefin Tuna Captains' logbook data were summed for each permit number in each year over all days of fishing to reduce the number of zero values. Only data from the general category permits were analyzed, which eliminated the harpoon category data, for which different regulations exist. The average month of fishing, average gear type, and average percentage of spotter plane usage were calculated by weighting observations by the number of days of effort. Average gear type was calculated by assigning gear codes of 1 to harpoon-type gear, 2 to mixed gear, and 3 to nonharpoon-type gear, and then computing a weighted average across all logbook records for a given year/captain/permit number combination. Three analyses of CPUEs were done from 1988 to 1993. The first analysis uses model 3, a general linear model on ln (CPUE+0.05), weighted by ln (days+1), back-transformed without the correction for the standard error (median estimate). The second analysis is the same as the first but with a σ2/2 correction (mean estimate). The third analysis is the effort-weighted, nonlinear, least-squares regression model (model 7). For all analyses, only gear and captain were significant

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An Assessment of Atlantic Bluefin Tuna TABLE 4-3  Estimates of giant bluefin tuna CPUE (catch per 100 line-hours) from rod and reel and handline, including number of trips and lower and upper 95% confidence limits. Year All Boats Number of Trips Lower Upper Only Boats for Which Tuna Were Sampled Number of Trips Lower Upper        Only Boats for Which Tuna Were Sampled in Two or More Years Number of Trips Lower Upper 83 4.25 1,589 3.09 5.82 N/A 0 - - N/A 0 - - 84 1.60 1,201 1.04 2.45 1.03 908 0.69 1.83 0.53 222 0.16 1.50 85 1.33 429 0.70 2.48 0.53 357 0.24 1.10 0.42 208 0.12 1.20 86 0.44 122 0.11 1.45 0.49 110 0.10 1.85 0.38 59 0.0004 3.26 87 0.55 1,917 0.37 0.83 0.38 1,275 0.25 0.58 0.37 788 0.20 0.64 88 1.01 760 0.60 1.68 1.09 508 0.59 1.98 1.12 352 0.52 2.37 89 0.85 1,199 0.54 1.32 0.72 746 0.45 1.20 0.47 418 0.21 0.97 90 0.78 1,635 0.48 1.16 0.85 1,067 0.56 1.29 0.86 616 0.47 1.54 91 0.77 1,478 0.51 1.15 0.53 1,050 0.34 0.81 0.32 413 0.13 0.68 92 0.99 1,010 0.62 1.55 0.57 430 0.29 1.10 0.67 251 0.24 1.72 N/A = data not available

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An Assessment of Atlantic Bluefin Tuna TABLE 4-4 Relative abundance of giant bluefin tuna from effort-weighted nonlinear least-squares regression (1992 = 1.00), including lower and upper 95% confidence limits. Year All Boats Lower Upper Only Boats for Which Tuna Were Sampled Lower Upper Only Boats for Which Tuna Were Sampled in Two or More Years Lower Upper 83 2.39 1.47 3.88 N/A N/A 84 1.32 0.80 2.17 1.28 0.83 1.98 1.18 0.65 2.17 85 1.05 0.60 1.83 0.88 0.55 1.43 1.17 0.67 2.06 86 0.72 0.25 2.11 0.56 0.22 1.43 0.96 0.38 2.52 87 0.62 0.33 1.18 0.58 0.33 0.99 0.72 0.38 1.35 88 1.10 0.62 1.94 1.01 0.62 1.66 1.45 0.85 2.49 89 0.97 0.55 1.71 1.15 0.73 1.83 1.76 1.04 2.96 90 0.76 0.44 1.33 0.86 0.54 1.40 1.41 0.84 2.35 91 0.99 0.59 1.67 0.99 0.63 1.56 1.23 0.65 2.30 92 1.00 0.60 1.71 1.00 0.60 1.67 1.00 0.49 2.04 N/A = data not available

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An Assessment of Atlantic Bluefin Tuna FIGURE 4-2  Western Atlantic Ocean giant bluefin tuna indices. (Table 4-5 and Figure 4-2). Month and plane use were significant before captain and gear were added to the model; therefore, captain and gear contain the information on month and plane use, making the latter two factors redundant. No significant annual trend was observed in the indices produced by any of the analyses. Comparison of Captains' Logbook Data and Rod and Reel Survey for Giant Bluefin Tuna Neither the captains' logbook data nor the rod and reel survey data show a trend in the standardized CPUEs of giant bluefin tuna during the years of overlap, 1988 through 1992 (Figure 4-2). Furthermore, annual trends restricted to experienced boats also were not significant. One interesting feature of Figure 4-2 is that the rod and reel index with greater restrictions on selection of data (marked RR 2) has a trend more similar to that of the captains' index, although the trends over time are not significant, as shown below. One concern in interpretation of CPUE indices is the potential for CPUEs to be overly optimistic regarding trends in abundance due to increasing catchability over years. Catchability can increase if improvements to gear, gains in skipper experience, or advances in technology for finding fish occur. In these results, experience was accounted for by deleting observations from vessels in which bluefin tuna catches were not sampled. Although this measure of experience is imperfect, the results did not differ from this factor. Further understanding of

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An Assessment of Atlantic Bluefin Tuna and Punt (1993). Although the movement rates and natural mortality rates are set to fixed constants for each analysis, this is not a static analysis; instead, it accommodates nonequilibrium dynamic trajectories of stock abundance. Changes with time in natural mortality or movement rates would likely require additional experimental data, such as from tagging experiments, or possibly further analysis of existing data. The transfer rates in (9) and (10) are annual rates, whereas the rates estimated in Chapter 3 are instantaneous. However, because the rates are small, they should be quite similar. The analysis was based on data for the period 1970 to 1992. Catch at age for the eastern component was not available for 1992, so it was assumed that the catches in that year were the same as in 1991. Movement rates assumed for the population were derived from the analysis of tagging data: 1% per year from west to east for all ages, and 2 and 3% per year from east to west for ages 6 and younger. The indices used for the tuning were the same indices used in the last SCRS assessments, with the exception of the U.S. rod and reel indices for small and large fish, which were revised for this assessment. The index derived from the captains' logbook data was not used because it was not completely independent of the U.S. rod and reel index for large fish and because it showed essentially the same trend as the latter. An additional inconsistency in the procedure applied to this analysis is that the selectivities by age used for both components of the population were estimated from results of the separable VPA, assuming isolated populations in the east and west. Table 4-8 shows the ratios of spawning stock (fish of ages 8 and older) abundances (N1993/N1975; N1993/N1988) and biomasses (B1993/ B1975; B1993/B1988) from different analyses. These analyses (cases), described below, have different levels of exchange and other variations to assess the effects of this variability on the results. Tables 4-9 and 4-10 list the vectors of exploitation rates and fishing mortalities by age in 1992. The contribution of each index to the total sum of squared residuals (a measure of the discrepancy between the predictions of the model and the data) is given in Table 4-11. Results indicate that as we allow for movement of fish between areas, it becomes difficult for the method to reconcile the trends suggested by the indices and the predictions of the model. The assessment tries to accommodate the large number of fish coming from the east. This is a consequence of the large differences in abundance of bluefin tuna on the eastern compared to the western side of the Atlantic Ocean: a contribution to the west of 2% (case 1, our base case) or 3% (case 2) of the abundance in the eastern Atlantic Ocean represents an important proportion of the western component. In years when either the recruitment in the east is high (e.g., 1983) or the indices in the west show a declining trend, the model tries to adjust to the large numbers of fish moving from east to west by estimating recruitment failures in the west for several years. Allowing exchange from the east results in a more optimistic appraisal of the status of the western component. Assuming annual exchange rates of 3%

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An Assessment of Atlantic Bluefin Tuna TABLE 4-8 Spawning stock abundance (N8+) and biomass (SSB) ratios (1993/1988 and 1993/1975) for the Western component of the Atlantic bluefin tuna.   Emigration rate N(8+) SSB Case East West 93/88 93/75 93/88 93/75 1 2%/yr 1%/yr 92.30% 18.10% 99.95% 24.54% 2 3%/yr 1%/yr 126.70% 36.10% 126.29% 45.70% 3 2%/yr 1%/yr 100.30% 21.30% 102.76% 27.35% 4 2%/yr 1%/yr 88.10% 20.60% 98.31% 25.28% 5 2%/yr 1%/yr 92.40% 18.20% 100.32% 24.65% 6 2%/yr 1%/yr 98.90% 20.70% 102.89% 26.98% 7 0%/yr 0%/yr 75.80% 13.80% 87.91% 19.09% 8 2%/yr 1%/yr 129.80% 43.00% 125.87% 50.85% Note: Case 1: Base case, Case 2: Increase eastern emigration rate, Case 3: Omit GOM index, Case 4: Vary natural mortality at age, Case 5: Delete Canadian CPUE index, Case 6: Increase catch of age 1 in Eastern Atlantic Ocean, Case 7: No migration (SCRS base case with data processing errors corrected), Case 8: Continue migration past age 6. from east to west and 1% from west to east (case 2), the indication is that the spawning stock in the western Atlantic Ocean has increased to 127% of the 1988 level, but is only 36% of the 1975 level (Table 4-8). A more conservative movement rate from east to west (2% annually, case 1) results in a spawning stock abundance about the same as the 1988 level (at about 92%), but is only 18% of the 1975 level. The predicted and observed values for the different indices for this particular case are shown in Figure 4-3. The overall fit to the indices is good, although there are discrepancies because the directions of trends differ among some indices. A number of sensitivity runs were made to assess the consequences of changing certain assumptions. One question that arises when we allow for mixing of the two stocks is related to spawning site fidelity. We cannot ascertain at this time whether fish spawn only in the areas where they were born or whether they exhibit a more opportunistic reproductive strategy, spawning wherever the environmental conditions are appropriate, regardless of where they are located. If the former hypothesis is correct, we cannot assume the indices derived from data in spawning areas of the west adequately represent the abundance of ages 8 and older. That is because these age classes would include a number of fish that are not present in the spawning areas. Therefore, a run was done in which the indices corresponding to the Gulf of Mexico were omitted (case 3). The results indicate virtually no change in spawning stock abundance since 1988, and a level representing 20% of the 1975 reported abundance. A separate analysis (also assuming annual movement rates of 2% east-west and 1% west-east) was done allowing for changes in age-specific natural mortality

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An Assessment of Atlantic Bluefin Tuna TABLE 4-9 Estimated exploitation rates by age in 1992 for the different cases.   Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8 West    Age 1 0.013 0.008 0.013 0.016 0.013 0.011 0.015 0.013 Age 2 0.067 0.042 0.066 0.081 0.067 0.060 0.074 0.069 Age 3 0.077 0.048 0.076 0.093 0.077 0.068 0.085 0.080 Age 4 0.041 0.022 0.040 0.052 0.040 0.038 0.044 0.038 Age 5 0.041 0.022 0.040 0.052 0.040 0.038 0.044 0.038 Age 6 0.058 0.045 0.066 0.069 0.057 0.062 0.062 0.077 Age 7 0.058 0.045 0.066 0.069 0.057 0.062 0.062 0.077 Age 8 0.112 0.046 0.093 0.159 0.112 0.096 0.175 0.055 Age 9 0.126 0.053 0.105 0.179 0.126 0.108 0.196 0.063 Age 10+ 0.108 0.045 0.090 0.154 0.108 0.093 0.170 0.054 East     Age 1 0.510 0.672 0.498 0.548 0.515 0.539 0.352 0.534 Age 2 0.584 0.743 0.571 0.622 0.588 0.613 0.414 0.608 Age 3 0.531 0.693 0.519 0.569 0.535 0.560 0.369 0.555 Age 4 0.683 0.805 0.653 0.615 0.639 0.984 0.464 0.503 Age 5 0.624 0.754 0.593 0.556 0.579 0.980 0.410 0.447 Age 6 0.376 0.495 0.351 0.322 0.340 0.932 0.223 0.247 Age 7 0.422 0.548 0.396 0.365 0.383 0.950 0.254 0.281 Age 8 0.176 0.211 0.120 0.289 0.175 0.187 0.198 0.077 Age 9 0.232 0.277 0.161 0.374 0.231 0.247 0.261 0.104 Age 10+ 0.611 0.683 0.468 0.804 0.608 0.636 0.658 0.327 rate: 0.5, 0.4, 0.3, and 0.2 for ages 1 through 4, and 0.1 for ages 5 and older (case 4). As expected, this assessment is closer to the results assuming a low exchange rate, because now the number of fish that move between east and west is much lower. The 1993 spawning stock5 abundance in numbers is estimated to be 88% relative to the 1988 level and 20% relative to the 1975 level. One caveat to this analysis is that the movement rates were estimated under an assumption that natural mortality was 0.14 for all ages; higher values of natural mortality in the younger ages cause higher estimates of movement rates. The consequences of deleting the Canadian tended-line CPUE from the set of indices (case 5) also were analyzed. This resulted in the same trends for the spawning stock abundance as indicated in the base case with 2% and 1% exchange rates (92% in 1993 relative to 1988, 18% relative to 1975). The effect of underreporting catches of young fish in the eastern Atlantic Ocean was assessed by increasing the catch of one-year-old fish in the eastern 5    In this section of the report, spawning stock is defined as fish on a given fishing ground (either the east Atlantic Ocean or the west Atlantic Ocean) that are capable of reproduction, but whose spawn localities are unknown.

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An Assessment of Atlantic Bluefin Tuna TABLE 4-10 Instantaneous fishing mortality rates by age in 1992 as estimated for the different cases considered in the VPA.   Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8 West   Age 1 0.014 0.009 0.014 0.017 0.014 0.012 0.016 0.014 Age 2 0.074 0.046 0.073 0.091 0.075 0.066 0.082 0.077 Age 3 0.086 0.053 0.085 0.105 0.086 0.076 0.095 0.089 Age 4 0.045 0.024 0.044 0.057 0.044 0.041 0.048 0.041 Age 5 0.045 0.024 0.044 0.057 0.044 0.041 0.048 0.041 Age 6 0.064 0.049 0.073 0.077 0.063 0.069 0.069 0.086 Age 7 0.064 0.049 0.073 0.077 0.063 0.069 0.069 0.086 Age 8 0.128 0.051 0.105 0.186 0.128 0.108 0.207 0.061 Age 9 0.145 0.058 0.119 0.212 0.145 0.123 0.235 0.070 Age 10+ 0.123 0.049 0.101 0.180 0.123 0.105 0.200 0.059 East   Age 1 0.781 1.238 0.753 0.870 0.791 0.849 0.470 0.837 Age 2 0.964 1.528 0.930 1.074 0.977 1.048 0.581 1.033 Age 3 0.829 1.314 0.800 0.924 0.840 0.901 0.499 0.888 Age 4 1.279 1.868 1.173 1.054 1.126 8.469 0.679 0.764 Age 5 1.080 1.577 0.991 0.890 0.950 7.151 0.573 0.645 Age 6 0.512 0.747 0.469 0.421 0.450 3.388 0.272 0.306 Age 7 0.597 0.872 0.547 0.492 0.525 3.952 0.317 0.357 Age 8 0.208 0.255 0.138 0.368 0.207 0.223 0.238 0.086 Age 9 0.285 0.351 0.189 0.508 0.283 0.306 0.326 0.118 Age 10+ 1.042 1.279 0.689 1.856 1.034 1.117 1.190 0.429 side by 50% (case 6). Results indicate, once more, that the spawning stock abundance is at virtually the same level as in 1988 (99%) and at a 20% level relative to 1975. Case 7 is the run assuming isolation of the two components of the population and as such, it represents the SCRS base case with data processing errors corrected. The methodology is essentially the same, but there are differences in the indices: the U.S. rod and reel indices for small and large fish have been revised, and the missing points in the Japanese longline index for the northwestern Atlantic Ocean have been added. In terms of the trends in spawning stock abundance, the assessment in case 7 offers about the same view of the situation of the stock (spawning abundance at 76% relative to 1988 and at 14% relative to 1975) with a better overall fit of the indices, compared to the 1993 SCRS assessment (spawning abundance at 78% relative to 1988 and at 15% relative to 1975). A comparison of the long-term trends in spawning stock biomass between cases 1, 2, and 7 is shown in Figure 4-4. Because of insufficient tagging of large bluefin tuna in the eastern Atlantic Ocean, the committee was not able to estimate movement rates for those fish, and we assumed a conservative zero probability of movement past age 6. A run

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An Assessment of Atlantic Bluefin Tuna TABLE 4-11 Contribution of each index and total weighted sum of squared residuals for each of the cases considered in the VPA.   Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8 West     Larval 0.544 0.723 — 0.533 0.591 0.567 0.505 0.770   JLL Small 0.295 0.508 0.398 0.269 0.322 0.313 0.263 0.436   JLL Medium 0.128 0.202 0.202 0.116 0.138 0.146 0.111 0.206   USRR Small 0.272 0.324 0.337 0.244 0.296 0.283 0.216 0.244   USRR Large 0.060 0.104 0.087 0.062 0.065 0.065 0.057 0.123   Can TL 0.076 0.129 0.113 0.082 — 0.084 0.063 0.161   JLL GoM 0.099 0.086 — 0.092 0.108 0.097 0.101 0.085   JLL NW-Atl 1.611 1.340 2.048 1.610 1.751 1.567 1.699 1.302   USLL GoM 0.141 0.173 — 0.137 0.154 0.148 0.127 0.175 East   JLL 0.075 0.076 0.096 0.079 0.081 0.075 0.076 0.073   FR PS 2 0.047 0.051 0.070 0.045 0.051 0.049 0.037 0.068   FR PS 3 0.047 0.045 0.074 0.040 0.051 0.048 0.044 0.075   ES Trap 71-81 0.121 0.121 0.159 0.116 0.132 0.121 0.126 0.126   ES Trap 82-91 0.040 0.041 0.053 0.042 0.043 0.040 0.041 0.049   ES BB 70-77 0.036 0.036 0.048 0.037 0.039 0.036 0.037 0.035   ES BB 78-91 0.058 0.063 0.074 0.061 0.063 0.060 0.057 0.058 Total 3.650 4.022 3.757 3.563 3.885 3.698 3.558 3.986

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An Assessment of Atlantic Bluefin Tuna FIGURE 4-3 Observed (solid line) and predicted (dashed line) values of indices for case 1.

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An Assessment of Atlantic Bluefin Tuna

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An Assessment of Atlantic Bluefin Tuna FIGURE 4-4 Comparison of the long-term trends in spawning stock biomass between cases 1, 2, and 7 (see Table 4-8 for case definitions). assuming that movement rates continue at the 2% annual level for ages beyond age 6 is shown as case 8. Trends in spawning stock abundance offer a more optimistic view (spawning stock abundance is 130% relative to 1988 and 43% relative to 1975). Overall, based on the analysis, estimates of fishing mortality for 1992 are much higher in the east than in the west (Table 4-10). The inclusion of movement exacerbates the difference in fishing mortality between east and west. The choice of indices, the change in natural mortality, and possible misreporting tend to be less important than transatlantic movement, except that altering natural mortality (case 4) had a large effect on older ages in the east and misreporting (case 6) caused a large increase for medium ages in the east. In terms of the fit to the indices, the assessment tends to favor exchange rates that are lower than the ones estimated from the analysis of the tagging data (Table 4-11). This conclusion is consistent with the results described by Butterworth and Punt (1993). As with estimating natural mortality, M, there is probably too little information in the indices to be able to estimate migration; hence, the sum of squares may not be a useful tool for comparison of the different cases. In practice, it is necessary to obtain natural mortality and migration rates from other independent sources and analyses, as was done in this study.

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An Assessment of Atlantic Bluefin Tuna DISCUSSION Current abundance of Atlantic bluefin tuna in the western Atlantic Ocean has been stable since 1988 based on the analyses above. That result is supported by the U.S. rod and reel indices of both small and giant bluefin tuna; by the U.S. captains' logbook data; and by Japanese longline indices for small, medium, and giant bluefin tuna. Indices that support a decline in abundance since 1988 are those based on data from the Gulf of Mexico (the larval index to some extent depending on the year of reference, but primarily the U.S. longline index and its 1992 data point). Support for an increase in abundance, particularly for the 8+ age group in the west, comes from acknowledging substantial immigration from the eastern Atlantic Ocean; however, that support could be undermined if migration rates are lower in the most recent years from the east; this would not have been detected from the analysis of the tagging data. Assessments also show that the absolute levels of abundance of the 8+ age stock in the western Atlantic Ocean are roughly two to five times greater than the levels estimated in the SCRS report. Trends of abundance in the western Atlantic Ocean between bluefin tuna in the Gulf of Mexico and those in the fisheries of the western Atlantic Ocean may diverge in the future. This possibility suggests that either different components of the Atlantic stock are being measured or there are errors in the indices. One hypothesis to account for the possible divergence is that the 8+ age group measured by western Atlantic fisheries is not representative of the spawners in the Gulf of Mexico, perhaps because the ocean fish are a mixture containing eastern Atlantic progeny, which exhibit spawning site fidelity and hence do not spawn in the west. Under this hypothesis, control of levels of spawning abundance in the Gulf of Mexico may not be easily accomplished by controls on fisheries in the western Atlantic Ocean: spawning site fidelity may occur with western Atlantic progeny, which may cause migrants in the eastern Atlantic Ocean to represent a portion of the Gulf of Mexico spawners. A second hypothesis to account for the divergence is that bluefin tuna are opportunistic spawners that will spawn whenever environmental conditions are favorable. Under this hypothesis, the environment in the Gulf of Mexico is variable and this variability causes spawners to represent a highly variable component of the 8+ age stock. An important assessment issue is how to predict future population sizes. Considerations such as definition of spawning stock, partitioning of recruitment between/among areas, and environmental factors could all be critical components of such work. Equally important in such predictions is the recognition that catch quotas have not been constant over the past several decades in the west but rather have been based on estimated changes in stock abundance. Adaptive management techniques can be applied to the projections. As a starting point, constant fishing mortality or harvest rate scenarios can be considered in lieu of constant catch policies as is currently the practice.

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An Assessment of Atlantic Bluefin Tuna Conclusions—Standardization Estimates of abundance are unchanged, on average, from 1988 to 1993 based on reanalyses of the three indices (two rod and reel indices and one captains' logbook index). The two indices on giant bluefin tuna (one rod and reel index and the captains' logbook index) are concordant. Furthermore, the selection criteria on classes of boats did not alter these conclusions, based on progressively more restrictive data exclusion to remove some inexperienced fishers. Transformations of catch rates according to logarithm of catch rate plus a large constant are inappropriate because they lack a biological foundation and contradict assumptions about independence of factors on catch rates. Using nonparametric tests, the Mann-Kendall S-test and Sen's slope estimator for the published SCRS indices, 12 indices were found to have no significant (slope) trends and four indices (see Table 4-6) had significant trends (all negative slopes) at (P ≤ 0.5). These tests also show that there are no significant trends in any of the CPUE data in Tables 4-1 to 4-5. Recommendations—Standardization A data management system should be established for catch indices that includes better documentation, quality control, central archiving, and error checking. A thorough, in-depth review of all indices from all areas of the Atlantic Ocean, Mediterranean Sea, and Gulf of Mexico is needed. Alternative methods for estimating stock abundance should be evaluated, including aerial survey, spawner surveys in the Florida Straits, purse seining for young bluefin tuna, and expanded larval fish surveys in the Gulf of Mexico. Selection criteria should be developed to create a rod and reel index for giant bluefin tuna, which excludes fishermen present in the captains' logbook index. That process would create two independent catch rate indices (the captains' logbook index and the modified rod and reel index on giant fish) that could both be used as tuning indices. Conclusions—Population Assessment The estimated spawning abundance of western Atlantic bluefin tuna has declined substantially (to about 20% of that in 1975) since the 1970's. The reasons for this decline are unknown, because the spawner-recruit relationship is uncertain. The current abundance of Atlantic bluefin tuna in the western Atlantic Ocean has been stable since 1988, in contrast to the roughly 50% decline in the age 8+ abundance reported in the 1993 ICCAT report. Reasons for the committee's view of current abundance result principally from two changes made to the SCRS assessments: (1) reanalysis and correction of some accidental errors

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An Assessment of Atlantic Bluefin Tuna in the calculation of the U.S. rod and reel index of abundance of bluefin tuna and (2) rejection of the two-stock hypothesis and subsequent reanalysis employing a two-area mixing model. Given the results of reanalysis, further reductions in catch quotas in the western Atlantic Ocean from 1992-1993 levels cannot be based on a conclusion of a decline in western Atlantic stock abundance since 1988. The mixing model points to the importance of bluefin tuna in the eastern Atlantic Ocean and Mediterranean Sea when evaluating the status and future of bluefin tuna in the western Atlantic Ocean. Even with relatively low mixing rates, the extremely large abundance of young tunas estimated recently in the eastern Atlantic Ocean causes the abundance of fishable age classes in the west to be strongly influenced by westward migrants. Fishing mortality in the east is perhaps four times greater than fishing mortality in the west. Considerable uncertainty exists about the relationship between fish on the fishing grounds and those on the spawning grounds. Recommendations—Population Assessment The committee recommends that: Given the revised view of stock structure, management strategies for the east and west should be revisited and should include minimum size limits, catch limits, and (spawning ground) area closures. Constant fishing mortality (that is, fixed at a constant annual rate for several years) may offer greater opportunity for rebuilding western stocks or reaching high long-term yields than constant catch quotas over many years. Future assessments of Atlantic bluefin tuna should be conducted with an assessment procedure that explicitly accounts for mixing. As a consequence, assessments of both eastern and western fisheries should be made together at each SCRS meeting. Given the sensitivity of results to the transfer rates, further inspection of the tagging data is warranted and further analysis to estimate rates should be undertaken. Alternative models to VPA, such as migratory catch age analysis and migratory stock synthesis analysis, should be considered.