**SCRS/2006/081:**

**Large Pelagics Survey Bluefin Tuna Length Validation Assessment**

**[Contributors]{.underline}:** David Van Voorhees, Ronald Salz, John
Foster, Joseph Desfosse, Craig Brown, Margo Schulze-Haugen, and
Christopher Rogers

**[Background]{.underline}**

The Large Pelagics Intercept Survey (LPIS) collects length data on
recreationally landed Atlantic bluefin tuna (ABT). The LPIS Procedures
Manual (prior to 2005) specified that interviewers should measure and
record the straight fork length (SFL) of ABTs, not the curved fork
length (CFL) that is used to define size classes for management
purposes. Recently, some members of the recreational and commercial
fishing industry have questioned whether or not this procedure has been
consistently followed in the field. Some individuals have reported
seeing LPIS interviewers measuring CFLs of landed bluefin tuna.
Therefore, they have raised a concern that the interviewers may actually
have been recording CFLs rather than SFLs. The curved fork length of a
given fish is greater than its straight fork length by some small factor
(typically between 1-5%). If such errors have occurred, then LPIS
estimates of landed weight of bluefin tuna by size category would most
likely be positively biased since length data are converted to weights
for landings estimates.

This evaluation was conducted to: 1) determine the extent to which CFLs
were mistakenly recorded, and the extent to which such errors may have
biased the overall ABT landed weight estimate, and 2) investigate the
effects that biased measurements could potentially have had on prior
stock assessments. The approach taken for the first part was to compare
LPIS length measurements with measurements from other data sources for
individual fish for which the length was recorded also. Two additional
sources of ABT length data -- the Maryland ABT Catch Card Program and
the NMFS Automated Landings Report System (ALRS) were examined. For both
the Maryland Catch Card Program and the ALRS, anglers are asked to
report the size of landed ABT as CFLs. The approach taken for the second
part of this evaluation was to simulate a scenario in which
[all]{.underline} LPIS length measurements since 1993 were assumed to be
erroneously recorded CFLs rather than SFLs.

# **LPIS and Maryland Catch Card Comparison**

Data from 2002-2004 were used to compare catch card length measurements
with LPIS measurements. The first step was to visually match records
representing individual fish, between the LPIS and Maryland catch card
datasets. Common variables used to determine if records matched were
date landed, HMS permit number, and vessel name. It was determined that
a total of 373 ABT measured in the LPIS were also reported on Maryland
catch cards for the years 2002-2004 (Table 1). LPIS lengths, which are
recorded in millimeters, were converted to inches to match catch card
lengths. The plot of LPIS recorded lengths versus Maryland catch card
reported lengths is shown below (Figure 1) for the three years combined.

Table 1. Number of ABT reported through the Maryland catch card program,
the number of ABT measured by the Large Pelagic Intercept Survey (in
Maryland), and matches between the two datasets, 2002-04.

  ------ ---------------- --------------- ---------------- ----------------
  Year   MD Catch Cards   LPIS Measured   Number Matched   Percent Matched

  2002   2327             175             131              74.9

  2003   2244             227             163              71.8

  2004   3548             84              79               94.1

  All    8119             486             373              76.7
  ------ ---------------- --------------- ---------------- ----------------

![](media/image1.wmf)

Figure 1. Plot of LPIS recorded lengths (in inches) versus reported
Maryland catch card lengths, 2002-04.

The straight line represents a slope of 1 going through the origin. If
both lengths were measured

and recorded as required for each program, it would be expected that 1)
most of the data points would fall above the line since straight fork
lengths (LPIS) are smaller than CFLs (MD catch cards), and 2) the
absolute difference between straight and curved length measurements
(taken on the same fish) should increase with fish size (i.e., as the
girth of the fish increases). Based on the above graph it is clear that
for many individual fish the relationship between LPIS and catch card
length measurements does not exactly match the expected relationship
between straight and curved length measurements. Plotting these pairs by
individual years also suggests there are differences between years in
terms of length validation results. In particular, a greater proportion
of data points are on or below the line in 2003 compared to 2002 or 2004
(Figures 2, 3 and 4).

![](media/image2.wmf)

Figure 2. Plot of LPIS recorded lengths (in inches) versus reported
Maryland catch card lengths, 2002.

![](media/image3.wmf)

Figure 3. Plot of LPIS recorded lengths (in inches) versus reported
Maryland catch card lengths, 2003.

![](media/image4.wmf)

Figure 4. Plot of LPIS recorded lengths (in inches) versus reported
Maryland catch card lengths, 2004.

A paired comparisons analysis was conducted to measure the mean
difference in lengths recorded by LPIS interviewers and HMS anglers on
Maryland catch cards for the same fish. Paired comparisons t-tests were
run to determine if the mean difference (measured in inches as catch
card length minus LPIS length) was significantly different from zero
(Table 2).

Table 2. Pairwise comparison t-tests of the mean difference between
Maryland catch card (curved fork) lengths and LPIS (straight fork)
lengths (note: difference = catch card length -- LPIS length)

  ----------- ----------- ------------ ----------- ----------- ------------
  Year        N           Mean         Std. Error  t value     Prob. \> \|
                          Difference                           t \|
                          (inches)                             

  2002        131         1.9137       0.259       7.39        \<0.0001

  2003        163         0.394        0.174       2.26        0.0251

  2004        79          0.776        0.407       1.91        0.0604

  All years   373         1.009        0.150       6.70        \<0.0001
  combined                                                     
  ----------- ----------- ------------ ----------- ----------- ------------

With all years combined, the mean difference (catch card length minus
LPIS length) was about one inch. Mean difference varied greatly by year
suggesting that the length measurement error rate (either as reported on
catch cards or recorded by LPIS interviewers) was also variable from
year to year during 2002-2004. Analysis of variance (ANOVA) confirmed
significant differences in the mean difference between 2002 and
2003-2004 (2003 and 2004 were not significantly different at alpha =
0.05).

The mean difference (catch card length minus LPIS length) was positive
and significantly different from zero for all years combined and for
2002 and 2003 individually (at the 0.05 significance level). For 2004
this mean difference was not significantly different from zero at the
0.05 level but was significant at the 0.10 level (p=0.06). While these
pairwise t-tests indicate that the mean catch card lengths are
significantly greater than the mean LPIS lengths (as would be expected),
they provide no indication of how the magnitude of this difference
compares to expected mean differences based on the true, unbiased
relationship between ABT curved and straight fork lengths. Therefore,
the next step was to compare these differences with expected differences
based on the relationship between ABT curved fork and straight fork
lengths over an equivalent range of fish sizes.

Two data sources which contained both curved and straight fork lengths
for ABT were used to calculate a linear regression of these two
variables: 1) 1996-2000 Large Pelagics Biological Survey (LPBS) data,
and 2) 2005 LPIS data. ABT greater than 73 inches CFL were not used in
this analysis since these landings are considered as part of the
commercial catch and were not part of the length validation study. The
regression line was forced through the origin (i.e., intercept = 0) to
assure that a zero value for curved fork length would correspond to a
zero value for straight fork length. The following equation, based on
all years 1996-2000 (LPBS) and 2005 (LPIS) combined, describes the
relationship between ABT straight fork length and curved fork length
(both in inches):

Straight fork length = 0.9728 X curved fork length (r^2^ = 0.999; p \<
0.001; n=1,308)

Using these regression parameters a predicted straight fork length was
calculated for each of the 373 (presumed) curved fork lengths in the
2002-2004 catch card datasets. Table 3 shows results of the pairwise
comparison t-tests for the mean of the difference between LPIS measured
lengths and the predicted straight fork lengths based on the regression
formula above. LPIS measured lengths exceeded the predicted straight
fork lengths by a mean difference of 0.264 inches for all years pooled
(2002-2004) and this difference was not significantly different from
zero at the 0.05 level (p=0.073). The standard error for this difference
was 0.146 which translates into an approximate 95% confidence interval
around this mean difference ranging from -0.025 to 0.554 inches. The
difference between LPIS length and predicted SFL (based on catch card
lengths) for individual observations with all years (2002-2004) combined
is shown in Figure 5. The difference between LPIS measured length and
predicted SFL expressed as a percent difference is shown in Table 4.

Investigation of the difference between observed (measured) and
predicted lengths by year revealed appreciable differences between years
(Figures 6-8). The mean difference was negative (i.e., predicted lengths
were greater than LPIS measured lengths) for 2002 comparisons. This
negative mean difference could not be explained by LPIS interviewers
accidentally recording curved instead of straight lengths. This
difference was significantly different from zero at the 0.05 level. The
mean difference for the 2004 data comparisons was positive (0.408
inches) but was not significantly different from zero at the 0.05 level
(p = 0.317). The mean difference for the 2003 data comparisons was both
positive (0.886 inches) and highly significant. The results of this
analysis suggest that if LPIS interviewers were recording curved lengths
instead of straight lengths this problem was more prevalent in 2003 than
either 2002 or 2004.

Table 3. Pairwise comparison t-tests of the mean difference between LPIS
measured lengths and predicted straight fork lengths based on MD catch
card lengths (note: difference = LPIS measured length -- predicted
straight fork length).

  ---------- --------- ------------ ---------- --------- --------- ----------
  Year       N         Mean         Variance   Std.      t value   Prob. \>
                       Difference              Error               \| t \|
                       (inches)                                    

  2002       131       -0.597       8.182      0.250     -2.37     0.019

  2003       163       0.886        4.798      0.172     5.16      \<0.0001

  2004       79        0.408        12.617     0.400     1.02      0.317

  All years  373       0.264        8.023      0.146     1.80      0.073
  combined                                                         
  ---------- --------- ------------ ---------- --------- --------- ----------

![](media/image5.wmf){width="5.072916666666667in"
height="2.7083333333333335in"}

Figure 5. Difference between LPIS measured length and predicted SFL
(based on MD catch card lengths) in inches for individual observations
with all years (2002-2004) combined.

Table 4. Mean LPIS measured length, mean difference between LPIS
measured length and predicted SFL based on MD catch card lengths, and
percent difference.

  ----------- --------------------- --------------------- ----------------
  Year        Mean LPIS Measured    Mean Difference       Percent
              Length (inches)       Between LPIS and      Difference
                                    Predicted             

  2002        46.51                 -0.597                -1.28 %

  2003        46.69                 0.886                 1.90 %

  2004        42.76                 0.408                 0.95%

  All years   45.79                 0.264                 0.58 %
  combined                                                
  ----------- --------------------- --------------------- ----------------

![](media/image6.wmf){width="5.072916666666667in"
height="2.7083333333333335in"}

Figure 6. Difference between 2002 LPIS measured length and predicted SFL
(based on MD catch card lengths) in inches for individual observations.

![](media/image7.wmf){width="5.072916666666667in"
height="2.7083333333333335in"}

Figure 7. Difference between 2003 LPIS measured length and predicted SFL
(based on MD catch card lengths) in inches for individual observations.

![](media/image8.wmf){width="5.072916666666667in"
height="2.7083333333333335in"}

Figure 8. Difference between 2004 LPIS measured length and predicted SFL
(based on MD catch card lengths) in inches for individual observations.

To further test the validity of LPIS lengths, the relationship between
LPIS (presumed) straight

fork lengths and Maryland catch card curved fork lengths, 2002-2004, was
compared to the relationship between straight fork lengths and curved
fork lengths from the combined LPBS (1996-2000) and LPIS (2005)
datasets. The comparison was made using an F-test to formally test for a
difference between the slope parameter from a linear regression of LPIS
measured lengths on Maryland catch card lengths and the slope parameter
from a linear regression of

straight lengths on curved lengths from the LPBS/LPIS combined datasets.
Both linear regressions were forced through the origin. The slope of the
fitted regression equation of straight fork length on curved fork length
from the LPBS and 2005 LPIS datasets was 0.9728 (r^2^ = 0.999; p \<
0.001; n=1,308). The 95% confidence interval around this slope parameter
ranged from 0.9716 (lower bound) to 0.9740 (upper bound). The slope of
the fitted regression equation of LPIS measured lengths on Maryland
catch card lengths for all years combined was 0.9758 (r^2^ = 0.996; p \<
0.0001; n= 373). The difference between these slope parameters was not
statistically significant (Prob. \> F = 0.332) (Table 5). Slope
parameters for individual years 2002 and 2003 were significantly
different from 0.9782 (2004 was not significantly different). However,
for 2002 the difference was in the opposite direction from what would be
expected if LPIS interviewers were substituting curved fork lengths for
straight fork lengths. Therefore, this difference could not be explained
by LPIS interviewers accidentally recording curved instead of straight
lengths. The difference in slopes for the 2003 data comparison were
highly significant and in the direction one would expect if LPIS
interviewers were substituting curved fork lengths for straight fork
lengths. These results suggest that if LPIS interviewers were recording
curved lengths instead of straight lengths this problem was more
prevalent in 2003 than either 2002 or 2004.

Table 5. Results of F-tests comparing the slope of the fitted regression
equation of LPIS measured lengths on Maryland catch card lengths with
the straight to curved fork length slope parameter of 0.9728.

+---------+--------+----------+--------+--------+--------+---------+
| Year    | N      | E        | 95%    |        | F      | Prob.   |
|         |        | stimated | Conf   |        | Value  | \> F    |
|         |        | Slope    | idence |        |        |         |
|         |        |          | Limit  |        |        |         |
|         |        |          |        |        |        |         |
|         |        |          | Low    |        |        |         |
|         |        |          | Bound  |        |        |         |
|         |        |          | Hi     |        |        |         |
|         |        |          | Bound  |        |        |         |
+---------+--------+----------+--------+--------+--------+---------+
| 2002    | 131    | 0.9577   | 0.9477 | 0.9676 | 9.07   | 0.003   |
+---------+--------+----------+--------+--------+--------+---------+
| 2003    | 163    | 0.9904   | 0.9832 | 0.9976 | 23.36  | \       |
|         |        |          |        |        |        | <0.0001 |
+---------+--------+----------+--------+--------+--------+---------+
| 2004    | 79     | 0.9786   | 0.9604 | 0.9967 | 0.40   | 0.531   |
+---------+--------+----------+--------+--------+--------+---------+
| All     | 373    | 0.9758   | 0.9697 | 0.9819 | 0.94   | 0.332   |
| years   |        |          |        |        |        |         |
| c       |        |          |        |        |        |         |
| ombined |        |          |        |        |        |         |
+---------+--------+----------+--------+--------+--------+---------+

Importantly, the results from comparing slopes mirror those found for
the pairwise comparison t-tests of the mean difference between LPIS
measured lengths and predicted straight fork lengths based on MD catch
card lengths (see above). Both analyses suggest that if LPIS
interviewers were recording curved lengths instead of straight lengths
this problem was more prevalent in 2003 than either 2002 or 2004. With
all three years combined neither test found a significant difference at
the alpha = 0.05 level.

**[LPIS and NMFS Automated Landings Report System]{.underline}**

Similar to the above analysis, ABT length measurements reported through
the NMFS Automated Landings Report System (ALRS) were compared with LPIS
measurements. Individual records from each dataset were visually matched
using date of landing, HMS permit number and vessel name. Unlike the
Maryland catch card program, the ALRS covers all LPIS states (except
Maryland) and therefore may be a more appropriate comparison for
assessing potential length measurement errors throughout the LPIS
interviewing range. Maine data were not used since the Maine Department
of Marine Resource conducts LPIS interviews, not the government
contractor. New Hampshire was not included since no matches were found
between LPIS and ALRS for the years 2002-2004.

After matching records it was determined that a total of 148 ABT that
were measured in the LPIS were also reported via the ALRS for 2002-2004
(Table 6). Small sample sizes in most states (and overall) made it
difficult to validate length measurements in any particular state. Since
overall sample sizes in 2003 and 2004 were also very small, all three
years were pooled for the analysis. LPIS lengths, which are recorded in
millimeters, were converted to inches to match ALRS lengths. The plot of
LPIS recorded lengths versus ALRS lengths is shown below for all three
years combined (Figure 9).

The straight line represents a slope of one going through the origin. If
both lengths were taken and reported as required for each program, it
would be expected that 1) most of the data points would fall above the
line since straight fork lengths (LPIS) are smaller than curved fork
lengths (ALRS reports), and 2) the absolute difference between straight
and curved length measurements (taken on the same fish) should increase
with fish size (i.e., as the girth of the fish increases). Based on
Figure 9 it is clear that, similar to the catch card comparison, for
many individual fish the relationship between LPIS and ALRS length
measurements does not match the expected relationship between straight
and curved length measurements.

Table 6. Number of records matched between ALRS and LPIS by state,
2002-04.

  ------------- -------------- -------------- -------------- --------------
  State         2002           2003           2004           All

  MA            6              4              2              12

  RI            3              15             1              19

  CT            0              3              1              4

  NY            1              3              1              5

  NJ            5              1              0              6

  DE            22             1              14             37

  VA            44             11             10             65

  All           81             38             29             148
  ------------- -------------- -------------- -------------- --------------

A paired comparisons analysis was conducted to measure the mean
difference in lengths recorded by LPIS interviewers and reported by HMS
anglers through the ALRS for the same fish. Paired comparisons t-tests
were run to determine if the mean difference (measured in inches as ALRS
length minus LPIS length) was significantly different from zero (Table
7). With all years and states combined, the mean difference (ALRS minus
LPIS length) was 0.205 inches and was not significantly different from
zero.

![](media/image9.wmf){width="4.020833333333333in" height="3.125in"}

Figure 9. Plot of LPIS recorded lengths (in inches) versus reported ALRS
lengths, 2002-2004.

Table 7. Pairwise comparison t-tests of the mean difference between ALRS
(curved fork) lengths and LPIS (straight fork) lengths (note: difference
= ALRS length -- LPIS length).

+----------+----------+-----------+----------+----------+-----------+
| Year     | N        | Mean      | Std.     | t value  | Prob. \>  |
|          |          | D         | Error    |          | \| t \|   |
|          |          | ifference |          |          |           |
|          |          | (inches)  |          |          |           |
+----------+----------+-----------+----------+----------+-----------+
| 2        | 148      | 0.205     | 0.284    | 0.72     | 0.472     |
| 002-2004 |          |           |          |          |           |
|          |          |           |          |          |           |
| combined |          |           |          |          |           |
+----------+----------+-----------+----------+----------+-----------+

Similar to the catch card analysis, the straight fork length versus
curved fork length regression

(i.e., straight fork length = 0.9728 X curved fork length) was used to
calculate a predicted straight fork length for each of the 148
(presumed) curved fork lengths in the 2002-2004 ALRS datasets. As
mentioned above, for all states north of Delaware sample sizes were
considered too small to analyze differences between predicted fork
length and LPIS lengths on a state-by-state basis. Data from New Jersey
through Massachusetts (n=46) were pooled for comparison with pooled data
from Delaware and Virginia (n=102). No significant difference was
detected in the mean difference between LPIS measured lengths and the
predicted straight fork lengths between these two groups (NJ-MA = 0.708,
DE/VA = 1.129, p = 0.491). This justified pooling all states in the
analysis.

Results of the pairwise comparison t-tests for the mean of the
difference between LPIS measured lengths and the predicted straight fork
lengths with all years and states pooled are shown in Table 8. LPIS
measured lengths exceeded the predicted fork lengths by a mean
difference of 0.998 inches for all years and states pooled (2002-2004)
and this difference was significantly different from zero. The standard
error for this difference was 0.282 which translates into an approximate
95% confidence interval around this mean difference ranging from 0.441
to 1.555 inches. The difference between LPIS length and predicted SFL
(based on ALRS lengths) for individual observations with all years
(2002-2004) combined is shown in Figure 10. The difference between LPIS
measured length and predicted SFL expressed as a percent difference is
shown in Table 9.

Table 8. Pairwise comparison t-tests of the mean difference between LPIS
measured lengths and predicted straight fork lengths based on ALRS
reported lengths (note: difference = LPIS measured length -- predicted
straight fork length).

+---------+--------+----------+--------+---------+--------+---------+
| Year    | N      | Mean     | Va     | Std.    | t      | Prob.   |
|         |        | Di       | riance | Error   | value  | \> \| t |
|         |        | fference |        |         |        | \|      |
|         |        | (inches) |        |         |        |         |
+---------+--------+----------+--------+---------+--------+---------+
| 20      | 148    | 0.998    | 11.731 | 0.282   | 3.54   | 0.0005  |
| 02-2004 |        |          |        |         |        |         |
|         |        |          |        |         |        |         |
| c       |        |          |        |         |        |         |
| ombined |        |          |        |         |        |         |
+---------+--------+----------+--------+---------+--------+---------+

![](media/image10.wmf){width="5.072916666666667in"
height="2.7083333333333335in"}

Figure 10. Difference between LPIS measured length and predicted SFL
(based on ALRS reported lengths) in inches for individual observations
with all years (2002-2004) combined.

Table 9. Mean LPIS measured length, mean difference between LPIS
measured length and predicted straight fork length based on ALRS
reported lengths, and percent difference.

+----------+--------------------+--------------------+---------------+
| Year     | Mean LPIS Measured | Mean Difference    | Percent       |
|          | Length (inches)    | Between LPIS and   | Difference    |
|          |                    | Predicted          |               |
+----------+--------------------+--------------------+---------------+
| 2        | 44.00              | 0.998              | 2.27 %        |
| 002-2004 |                    |                    |               |
|          |                    |                    |               |
| combined |                    |                    |               |
+----------+--------------------+--------------------+---------------+

# 

To further test the validity of LPIS lengths, the relationship between
LPIS (presumed) straight

fork lengths and ALRS curved fork lengths, 2002-2004, was compared to
the relationship between straight fork lengths and curved fork lengths
from the combined LPBS (1996-2000) and LPIS (2005) datasets. The
comparison was made using an F-test to formally test for a difference
between the slope parameter from a linear regression of LPIS measured
lengths on ALRS lengths and the slope parameter from a linear regression
of straight lengths on curved lengths from the LPBS/LPIS combined
datasets. Both linear regressions were forced through the origin. The
slope of the fitted regression equation of straight fork length on
curved fork length from the LPBS and 2005 LPIS datasets was 0.9728 (r^2^
= 0.999; p \< 0.001; n=1,308). The 95% confidence interval around this
slope parameter ranged from 0.9716 (lower bound) to 0.9740 (upper
bound). The slope of the fitted regression equation of LPIS measured
lengths on ALRS lengths for all three years combined was 0.99934 (r^2^ =
0.994; p \< 0.0001; n= 148). The difference between these slope
parameters was statistically significant (Prob. \> F = 0.0013) (Table
10) and in the direction one would expect if LPIS interviewers were
substituting curved fork lengths for straight fork lengths.

Table 10. Results of F-tests comparing the slope of the fitted
regression equation of LPIS measured lengths on ALRS lengths with the
straight to curved fork length slope parameter of 0.9728.

+---------+--------+----------+--------+--------+--------+---------+
| Year    | N      | E        | 95%    |        | F      | Prob.   |
|         |        | stimated | Conf   |        | Value  | \> F    |
|         |        | Slope    | idence |        |        |         |
|         |        |          | Limit  |        |        |         |
|         |        |          |        |        |        |         |
|         |        |          | Low    |        |        |         |
|         |        |          | Bound  |        |        |         |
|         |        |          | Hi     |        |        |         |
|         |        |          | Bound  |        |        |         |
+---------+--------+----------+--------+--------+--------+---------+
| 20      | 148    | 0.9934   | 0.9810 | 1.0058 | 10.77  | 0.0013  |
| 02-2004 |        |          |        |        |        |         |
|         |        |          |        |        |        |         |
| c       |        |          |        |        |        |         |
| ombined |        |          |        |        |        |         |
+---------+--------+----------+--------+--------+--------+---------+

Importantly, the results from comparing slopes mirror those found for
the pairwise comparison t-tests of the mean difference between LPIS
measured lengths and predicted straight fork lengths based on ALRS
lengths (see above).

**[Level of Analysis]{.underline}**

The analyses above suggest that temporal and geographic variation exist
in terms of differences between LPIS length measurements and predicted
SFLs (based on catch cards and ALRS). This raises the question as to
what temporal/geographic scale should such differences, and potential
length measurement error rates, be evaluated. Potential error rates
could, theoretically, be calculated and applied for particular
state/year strata combinations. However, from a practical standpoint
this is difficult to justify statistically since sample sizes are very
small within many of these strata. It may also be preferable to apply a
uniform correction factor across the entire LPS area and time frame
under consideration from a management perspective.

Since the LPIS-ALRS comparison did not cover Maine and New Hampshire and
for several other states sample sizes were very small, the following
assumption is made for the purpose of examining the implications of a
potential length measurement error rate:

-   The presumed overall LPIS-ALRS length measurement error rate
    represents a valid estimate of the error rate in Maine and New
    Hampshire as well as other states where sample sizes for this
    analysis were small.

To arrive at a single potential length measurement error rate for all
LPS states (Maine through Virginia) and years, the overall length
difference (LPIS versus predicted SFLs) from the LPIS-MD catch card
comparison (which only covers ABT length measured in Maryland) was
weighted and averaged with the LPIS-ALRS length difference. Weighting
factors were based on total estimated ABT recreational landings (in
numbers) from the 2002-2004 LPS (Table 11). ABT in the large medium and
giant categories were not included in the weighting procedure since
these are considered commercial and were not part of the length
validation assessment.

Table 11. Total recreational bluefin tuna landings (young school,
school, large school and small medium size classes) used for weighting
of length measurement adjustment factors.

+------------------------+----------------------------------+---------+
| Geographic Area        | Total ABT Landings 2002-2004     | Percent |
|                        |                                  |         |
|                        | (numbers of fish)                | Weight  |
+------------------------+----------------------------------+---------+
| Maryland               | 13,087                           | 27.6%   |
+------------------------+----------------------------------+---------+
| Maine through Virginia | 34,371                           | 72.4%   |
|                        |                                  |         |
| (excluding Maryland)   |                                  |         |
+------------------------+----------------------------------+---------+
| Total                  | 47,458                           | 100%    |
+------------------------+----------------------------------+---------+

LPIS measured lengths exceeded the predicted fork lengths based on the
Maryland catch card data by a mean difference of 0.264 inches for all
years pooled (2002-2004). LPIS measured lengths exceeded the predicted
fork lengths based on the ALRS data by a mean difference of 0.998 inches
for all years pooled (2002-2004). The weighted mean difference is
calculated as follows:

Mean Difference (weighted) = (0.264 X 0.276) + (0.998 X 0.724) = 0.795
inches

The weighted mean LPIS length is calculated as follows:

Mean LPIS length (weighted) = (45.79 X 0.276) + (44.0 X .724) = 44.494
inches = 113.01 cm

Mean Predicted Straight Fork Length = 44.494 -- 0.795 = 43.699 inches =
111.00 cm

The percent difference between the mean LPIS length and the predicted
straight fork length is 1.779%.

**[Conversion to Weight-based Adjustment Factor]{.underline}**

The next step was to convert from a length-based adjustment factor
(0.795 inches per fish) to a weight-based adjustment factor. Data from
the 1998-2000 Large Pelagics Biological Survey (LPBS) were used to
compute a weight-length conversion formula. This represents the three
most recent years of the LPBS data collection. After thorough
error-checking and outlier reduction analysis, a total of 409
observations were available for the regression. ABT greater than 73
inches CFL were not used in this analysis since these landings are
considered as part of the commercial catch and were not part of this
length validation study. A simple linear regression was computed of the
log of weight (kg) and the log of length (SFL cm):

-   Log(weight kg) = m X log(SFL cm) + b

> (Where m = slope, and b = intercept)

-   Log(weight kg) = 2.78986 X log(SFL cm) -- 4.296

-   Weight kg = 0.0000506 X (SFL cm) ^2.790^

Using this weight-length conversion formula, the estimated mean ABT
weight based on the mean LPIS length measurement is:

-   Weight kg = 0.0000506 X (113.01) ^2.790^ = 27.061 kg

The estimated mean ABT weight based on the mean predicted SFL is:

-   Weight kg = 0.0000506 X (111.00) ^2.790^ = 25.740 kg

The percent difference between the estimated mean weight based on LPIS
lengths and the estimated mean weight based on predicted SFL is 4.88%.
It should be noted that this method could produce additional bias if the
size distribution of the samples are in fact not representative of the
actual catch.

# **Limiting Assumptions**

It is important to identify the limiting assumptions of this evaluation,
particularly if these results are to be used to make adjustments to
historical landings data and/or for future ABT quota allocations.
Failure to meet the assumptions would change the provisional results
presented and could well invalidate the method described for estimating
potential length measurement error rates.

**1.A. Maryland catch card length measurements and LPIS length
measurements were independent.**

**1.B. ALRS length measurements and LPIS length measurements were
independent.**

One important assumption is that the two length measurements being
compared are independent of one another. For many observations, the LPIS
length measurement was identical to the length recorded by anglers on
the catch cards or reported using ALRS. For several other matches the
two lengths were close enough that they could be explained by angler
rounding error on the catch cards or ALRS (i.e., LPIS lengths are
recorded in millimeters while anglers typically round to the nearest
inch or half-inch). Two possible explanations for identical (or nearly
identical) LPIS and catch card lengths for the same fish are: 1) LPIS
interviewers incorrectly recorded a curved length rather than a straight
length, or 2) anglers were completing the catch cards using the
measurements made by the LPIS interviewers, irregardless of whether
these were curved or straight lengths. Only if we assume that the two
length measurements were largely independent of one another can we
reject the second explanation that anglers were recording catch card
lengths based on information provided to them by LPIS interviewers. The
assumption of independence is further complicated by the fact that LPIS
interviewers from 2002-2004 were instructed, as a courtesy, to measure
the curved fork length of a bluefin tuna if asked to do so by an
interviewed captain or angler (even though they were only supposed to
record the straight fork length on the standard data form).

**2.A. Angler reported Maryland catch card lengths represent fairly
accurate measurements of ABT curved fork lengths, and if there are
sources of error associated with these measurements the error is
random.**

**2.B. Angler reported ALRS lengths represent fairly accurate
measurements of ABT curved fork lengths, and if there are sources of
error associated with these measurements the error is random.**

There is reason to believe that some anglers "ballpark" ABT length
information on the catch cards or in reports to the ALRS. In addition,
catch card lengths are generally reported in whole inch (or sometimes
half-inch) increments and only rarely with a higher degree of precision.
Thus, another necessary assumption is that any errors (rounding,
digit-bias or otherwise) associated with angler self-reported lengths on
catch cards (or to ALRS) are random and essentially cancel each other
out (e.g., overestimations and underestimations occur with the same
frequency). By contrast, if, for example, anglers more frequently
overestimate rather than underestimate ABT lengths, such a bias could
affect the validity of this analysis.

In 2005 LPIS interviewers recorded both straight fork lengths (SFLs) and
curved fork lengths (CFLs) for bluefin tuna. LPIS interviewers will
continue to collect both straight and curved lengths on ABT in future
years to avoid any ambiguity regarding which lengths were actually
measured in the field. This will also provide additional data for
computing a straight to curved length ratio. LPIS 2005 curved length
measurements were compared with Maryland 2005 catch card and ALRS 2005
curved length measurements to test the assumption that angler reported
Maryland catch card lengths and ALRS lengths from 2002-2004 represent
fairly accurate, unbiased measurements of ABT CFLs. The LPIS and catch
card/ALRS datasets were visually matched to identify individual fish
that had been measured and recorded by both an LPIS interviewer and an
angler or captain. The method used to match records was identical to
that used to match data from the 2002-2004 datasets.

A total of 126 ABT had CFLs recorded through both the Maryland catch
card program and the LPIS. A pairwise t-test was used to compare
differences between the CFLs recorded for the two data collection
methods. The mean Maryland catch card CFL was 0.79 inches greater than
the mean LPIS CFL. However, these means were not significantly different
at the alpha=0.05 level (df = 125, t = 1.97, p = 0.051). These results
suggest that the 2005 catch card lengths represent fairly accurate
measurements of ABT CFLs, and if there are sources of error associated
with these measurements the error is random. The fact that catch card
lengths were larger, on average, than LPIS CFLs suggests that anglers
have a tendency to round up to the nearest inch when reporting lengths
on catch cards (LPIS interviewers record to the nearest millimeter).

In 2005 only 14 ABT had CFLs both reported through the ALRS and recorded
by LPIS interviewers. This sample size was deemed too small to perform
any meaningful statistical analysis. Therefore, it was not possible to
directly test the assumption that ALRS lengths represent fairly
accurate, unbiased measurements of ABT CFLs.

The 2005 data provide tentative support for accepting the assumption
that angler reported Maryland catch card lengths and ALRS lengths from
2002-2004 are unbiased, and if there are sources of error associated
with these measurements the error is random. However, support for this
assumption is predicated on acceptance of two additional limiting
assumptions:

-   Angler CFLs recorded on Maryland catch cards from 2002-2004 were at
    least as accurate as angler CFLs recorded on Maryland catch cards in
    2005.

-   Angler CFLs reported via ALRS are at least as accurate as CFLs
    recorded by Maryland anglers on catch cards.

If one assumes that the LPIS measurements were recorded accurately,
irrespective of whether they were SFLs or CFLs, then an angler reported
length should never be smaller than an LPIS length from the same fish,
except for rounding differences. If, after correcting for rounding, an
angler reported length (via ALRS or catch card) is still smaller than an
LPIS length, the likeliest explanation is that the angler length is
inaccurate. More than one-third (35%) of the 148 ALRS lengths were
smaller than the LPIS length for the same fish even after accounting for
rounding. By comparison, after accounting for rounding, only 20% of the
self-recorded catch card curved lengths were actually smaller than the
associated LPIS length. Therefore, these results suggest that ALRS
lengths are not as accurate as Maryland catch card lengths.

**3. The relationship between ABT curved and straight fork lengths,
based on LPBS data from 1996-2000 and LPIS data from 2005, is a good fit
for the 2002-2004 length measured ABT.**

The relationship between straight and curved fork lengths may vary from
year to year depending on a number of factors including average fish
size, condition, and geographic and temporal distribution throughout the
fishing season. Ideally, we would want to use data from the years in
question (i.e., 2002-2004) to establish the curved-straight length
relationship. However, since the LPBS was not conducted from 2002-2004,
the regression was based on pooled data from the most recent five years
of LPBS data, 1996-2000. LPBS data were combined with LPIS data from
2005, the first year that both curved and straight fork lengths were
collected on the LPIS. The ratio of straight fork length to curved fork
length computed from 2005 LPIS was nearly identical to the same ratio
based on 1996-2000 Large Pelagics Biological Survey (LPBS) data. This
provided support for the assumption that the ratio used for this
assessment was a good fit for the 2002-2004 data.

**4. The difference between the expected deviation and the mean sample
deviation represents a measure of the relative frequency of curved
lengths being incorrectly substituted for straight lengths in the LPIS
data.**

Estimation of an actual error rate (i.e., percent of curved lengths
being incorrectly substituted for straight lengths in the LPIS data)
from individual matched records would have been extremely sensitive to
unknown measurement errors. Instead, this analysis focused on
differences between mean sample lengths (LPIS lengths versus expected
straight fork lengths). Therefore, another necessary assumption of this
analysis is that the difference between these sample means represents a
fairly accurate measure of this error rate.

**[Impact of Length Measurement Errors on ABT Stock
Assessment]{.underline}**

The approach taken for this component was to simulate a scenario in
which all LPIS length measurements from 1993 on were assumed to be
curved fork lengths rather than straight. The U.S. rod and reel caught
ABT lengths less than 178 cm in the catch-at-length data used for the
2002 ICCAT ABT stock assessment were multiplied by an adjustment factor
of 0.955 (the standard factor which has been used for previous
conversions from curved to straight length) representing a 4.5%
reduction. A new a catch-at-age matrix was created following the usual
procedures. Finally, a virtual population analysis (VPA) was conducted,
using the same inputs as were used for the 2002 ICCAT ABT stock
assessment except for the changes to the catch-at-age matrix and
corresponding weight-at-age. The VPA results were then compared to the
results obtained from the 2002 stock assessment.

Changes to the VPA estimates of historical abundance and fishing
mortality results appear to be minor, even given the assumption that all
LPIS length measurements taken since 1993 were curved rather than
straight. The largest differences appear in the recruitment trends
(Table 12 and Figure 11), which are shown through 1998 since the last
several years are not predicted well by the VPA. Only 1997 shows a
difference greater than 6%. The differences in spawning stock biomass
(SSB, Table 13 and Figure 12)) and fishing mortality (ages 8+, Table 14
and Figure 13) trends are even smaller. Changes to the VPA estimates are
likely to be even smaller than estimated here since this analysis
assumed a 4.5% reduction (SFL/CFL = 0.955) in LPIS lengths while the
regression calculated from LPBS and 2005 LPIS data predicted only a 2.7%
difference between SFL and CFL. It appears unlikely that any bias
resulting from measurements of curved rather than straight lengths in
the LPIS would have altered stock status evaluations. This is not
surprising, since the VPA is based on estimates of catch in numbers of
fish at age, a feature not very sensitive to the issues discussed above.
More importantly, however, are the implications of assuming different
average weight at age for future projections of TAC levels. NMFS will
attempt to collect more ABT lengths and weights in 2006 to test the
validity of the length-weight relationships used for stock assessment
purposes.

Table 12. Recruitment trends showing difference between 2002 stock
assessment and adjusted assessment assuming all LPIS length were
recorded as curved instead of straight.

  ------- ------------ ---------- -------- ------- ------------ ---------- --------
  year    2002         Assuming   \%       year    2002         Assuming   \%
          Assessment   Bias       change           Assessment   Bias       change

  1970    339984       339769     -0.1%    1985    74486        74586      0.1%

  1971    266988       266725     -0.1%    1986    91726        91846      0.1%

  1972    235103       234738     -0.2%    1987    68750        68343      -0.6%

  1973    152763       151818     -0.6%    1988    91673        91897      0.2%

  1974    487089       487139     0.0%     1989    50771        50151      -1.2%

  1975    143588       143613     0.0%     1990    90988        89979      -1.1%

  1976    136118       136154     0.0%     1991    80782        80304      -0.6%

  1977    86557        86572      0.0%     1992    47480        46641      -1.8%

  1978    55327        55335      0.0%     1993    46026        46978      2.1%

  1979    81449        81500      0.1%     1994    24204        25586      5.7%

  1980    67036        67087      0.1%     1995    143648       138895     -3.3%

  1981    61460        61502      0.1%     1996    85494        80393      -6.0%

  1982    57357        57423      0.1%     1997    56820        69636      22.6%

  1983    96243        96319      0.1%     1998    150680       141872     -5.8%

  1984    68343        68406      0.1%                                     
  ------- ------------ ---------- -------- ------- ------------ ---------- --------

Figure 11. Plots of estimated ABT recruitment trends from the 2002 ICCAT
stock assessment (solid line) and from a run assuming that all LPS
measurements were curved fork lengths rather than straight (dashed
line).

Table 13. Spawning stock biomass trends showing difference between 2002
stock assessment and adjusted assessment assuming all LPIS length were
recorded as curved instead of straight.

  ------- ------------ ---------- -------- ------- ------------ ---------- --------
  Year    2002         Assuming   \%       year    2002         Assuming   \%
          Assessment   Bias       change           Assessment   Bias       change

  1970    50033        50932      1.8%     1986    11316        11354      0.3%

  1971    45236        46075      1.9%     1987    10141        10176      0.3%

  1972    45281        46165      2.0%     1988    9613         9648       0.4%

  1973    43241        44028      1.8%     1989    8858         8893       0.4%

  1974    44134        44837      1.6%     1990    8638         8675       0.4%

  1975    37905        38446      1.4%     1991    7899         7936       0.5%

  1976    36340        36751      1.1%     1992    7645         7684       0.5%

  1977    31017        31373      1.1%     1993    8099         8143       0.5%

  1978    28400        28700      1.1%     1994    8352         8399       0.6%

  1979    22514        22736      1.0%     1995    8880         8935       0.6%

  1980    21304        21446      0.7%     1996    8332         8390       0.7%

  1981    18825        18932      0.6%     1997    8741         8809       0.8%

  1982    17973        18027      0.3%     1998    8693         8770       0.9%

  1983    17575        17626      0.3%     1999    7616         7701       1.1%

  1984    14973        15017      0.3%     2000    6872         6970       1.4%

  1985    11930        11968      0.3%     2001    5024         5124       2.0%
  ------- ------------ ---------- -------- ------- ------------ ---------- --------

Figure 12. Plots of estimated ABT spawning stock biomass (SSB) trends
from the 2002 ICCAT stock assessment (solid line) and from a run
assuming that all LPS measurements were curved fork lengths rather than
straight (dashed line).

Table 14. Fishing mortality trends showing difference between 2002 stock
assessment and adjusted assessment assuming all LPIS length were
recorded as curved instead of straight.

  ------- ------------ ---------- -------- ------- ------------ ---------- --------
  year    2002         Assuming   \%       year    2002         Assuming   \%
          Assessment   Bias       change           Assessment   Bias       change

  1970    0.0177       0.0177     0.0%     1986    0.1333       0.1333     0.0%

  1971    0.0780       0.0770     -1.3%    1987    0.1383       0.1380     -0.2%

  1972    0.0353       0.0347     -1.9%    1988    0.1883       0.1880     -0.2%

  1973    0.0443       0.0440     -0.8%    1989    0.2207       0.2197     -0.5%

  1974    0.0607       0.0597     -1.6%    1990    0.2127       0.2120     -0.3%

  1975    0.0640       0.0633     -1.0%    1991    0.2307       0.2300     -0.3%

  1976    0.0820       0.0817     -0.4%    1992    0.2077       0.2067     -0.5%

  1977    0.1007       0.1007     0.0%     1993    0.1893       0.1883     -0.5%

  1978    0.0937       0.0940     0.4%     1994    0.1693       0.1683     -0.6%

  1979    0.1133       0.1130     -0.3%    1995    0.1773       0.1760     -0.8%

  1980    0.1657       0.1653     -0.2%    1996    0.1663       0.1653     -0.6%

  1981    0.1997       0.1993     -0.2%    1997    0.1837       0.1827     -0.5%

  1982    0.0647       0.0647     0.0%     1998    0.2407       0.2383     -1.0%

  1983    0.1143       0.1143     0.0%     1999    0.2940       0.2910     -1.0%

  1984    0.1187       0.1187     0.0%     2000    0.2763       0.2730     -1.2%

  1985    0.1743       0.1743     0.0%     2001    0.4150       0.4070     -1.9%
  ------- ------------ ---------- -------- ------- ------------ ---------- --------

Figure 13. Plots of estimated ABT fishing mortality trends on ages 8 and
above (F~ages\ 8+~) from the 2002 ICCAT stock assessment (solid line)
and from a run assuming that all LPS measurements were curved fork
lengths rather than straight (dashed line).

**[Management Alternatives]{.underline}**

Survey data errors are best addressed as close to the source (i.e., the
interviewer) and collection date as possible. The above assessment
highlights the difficulties associated with validating historical
fisheries survey data collected up to three years ago by multiple
interviewers. The LPIS contractor claims that their interviewers were
measuring and recording ABT straight fork lengths. Some fishing industry
members claim that curved fork lengths were being measured and recorded
by LPIS interviewers. Management must decide if an adjustment to
historical bluefin tuna landings data due to this potential measurement
error is warranted at this time. Regardless of this decision, the
straight length / curved length debate will not be an issue in future
years (2005 and beyond) now that LPIS interviewers are instructed to
collect both lengths on all ABT measured.

Several alternatives are available to management given the inherent and
un-quantified uncertainty associated with these results. Management
alternatives include the following:

**Alternative #1**: No action alternative.

If the limiting assumptions that this evaluation is predicated upon are
not accepted then management may chose the no action alternative. That
is, if there is reason to believe that any of the assumptions have been
violated (e.g., that angler reported ABT lengths on catch cards or
through ALRS are biased and/or that these lengths are not independent
from matched LPIS lengths), any adjustment to historical ABT landings
based on these results may be biased. Justification for supporting this
alternative could be derived from the following findings: 1)
inconsistent (even contradictory) results across years, 2) high
variability in comparisons between angler lengths and interviewer
lengths, 3) low sample sizes and limited coverage of the available data
(across state/year/interviewer strata) to test for measurement bias, and
4) the likely violation of one or more of the limiting assumptions.

Both curved fork and straight fork lengths are difficult to measure
accurately without proper training and equipment. Considering that for a
given fish the difference between these two measures is proportionally
small (less than 3% on average per fish) even a minor measurement bias
could significantly alter the results of this evaluation. Testing the
validity of angler recorded Maryland catch card lengths provided only
marginal support for the assumption that these lengths are unbiased
curved fork lengths. The validity of angler reported ALRS lengths could
not be tested due to the small sample size. However, comparisons with
LPIS measurements did suggest that ALRS reported lengths were not as
accurate as catch card lengths. If this is the case, it is highly likely
that the assumption that angler reported ALRS lengths represent unbiased
curved fork lengths is violated.

Since the LPIS-ALRS length comparison analysis results were weighted
more heavily than the LPIS-catch card comparison results (72.4% versus
27.6%), even a slight bias in the ALRS reported lengths could
significantly impact the adjustment factor results. In addition, the
LPIS-catch card results indicate no clear, consistent pattern regarding
LPIS mis-measurements across years. When compared to MDCC predicted
straight lengths, LPIS lengths were significantly smaller in 2002,
significantly larger in 2003, not significantly different in 2004, and
not significantly different with all three years pooled.

The claims by some anglers and fishing industry representatives that
they have observed curved lengths being recorded have been given strong
credence. NMFS has expended considerable resources researching these
claims and attempting to validate LPIS length measurements. If the no
action alternative is chosen by management this should not be
interpreted as a definitive conclusion that no biased measurements (CFLs
rather than the expected SFLs) were taken by LPIS interviewers. Rather,
selection of this alternative would indicate that the agency believes
that available data and analyses are insufficient to determine to what
extent curved lengths rather than straight may have been recorded, and
how that rate may have varied across years and areas.

**Alternative #2**: Apply an adjustment factor of 4.88% to the ABT
recreational landings weight (Maine through Virginia, fish less than 73
inches CFL) over the years 2002-2004.

Fishing industry member claims that LPIS interviewers were recording
curved lengths instead of straight lengths are directed at the 2002-2004
LPS survey years. If all of the limiting assumptions (see above)
associated with this analysis are accepted, management can apply an
adjustment factor to correct for over-estimated landings weight
estimates for these three years. The weight of 2002-2004 recreational
landings of ABT (Maine through Virginia, fish less than 73 inches CFL)
could be reduced by 4.88%.

The sensitivity analysis performed on the stock assessment shows that
even if all LPIS lengths are treated as curved fork lengths, (either
over all years or just 2002-2004), changes to the VPA results in terms
of recruitment trends, fishing mortality and spawning stock biomass will
be relatively minor. It is, therefore, unlikely that in hindsight this
presumed bias would have resulted in any significant impacts on stock
status evaluations.

**Alternative #3**: Apply an adjustment factor of 4.88% to the ABT
recreational landings weight (Maine through Virginia, fish less than 73
inches CFL) over the years 1995-2004.

If all of the limiting assumptions associated with this analysis are
accepted, management can apply an adjustment factor to correct for
over-estimated landings weight for all LPS survey years during which
CFLs may have been substituted for SFLs. That is, if LPIS interviewers
were incorrectly recording CFLs from 2002-2004, one may presume that
they were also erroneously recording CFLs in previous survey years.
While the Large Pelagics Survey has been conducted since 1986, the use
of curved fork lengths for management regulations began in 1995. Since
straight fork lengths were used for management prior to 1995, it is
presumed that if there was any confusion amongst LPIS interviewers
regarding which length to record this confusion began in 1995.

Alternative #3 is riskier than alternative #2 because: 1) it requires
the additional assumption that ABT length measurement error rates from
1995-2001 were similar to those from 2002-2004, and 2) if any of the
original assumptions above turn out to be false, all LPS ABT landings
weight data from 1995-2004 will be adjusted by an inaccurate correction
factor, rather than just three years of data as would be the case with
Alternative #2.