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Fishery Bulletin 95 ( 1 ), 1997 
from the LTSj fit (second column), and the LTS 9 fit 
(last column). The open symbols indicate which data 
points were identified as outliers according to the t- 
test criterion mentioned previously. The LTS : regres- 
sion, which gives equal consideration to all index 
series, identified 9 outliers (11% of the total index 
data points). The LTS 2 approach, which gives more 
weight to the better-fitting series, identified the same 
9 observations as outliers, and an additional 8 (21% 
of the total number of data). The 1978 estimate from 
the larval index stands out as a particularly large 
outlier (Fig. 4). But perhaps more importantly in 
terms of the effect on the SPA results, the 1992 data 
point for the Japanese Northwest Atlantic longline 
index, is also identified as a large outlier. That is, 
because of the convergence properties of the ADAPT 
approach, the more recent data tend to have a larger 
impact on the estimates of current stock status. 
Figure 5 shows the estimated stock size trajecto- 
ries for 3 age groupings that ICCAT assessments fo- 
cus on: small fish (ages 2 to 5), medium fish (ages 6 
and 7), and spawners (ages 8 and older). The solid 
line without symbols represents the ini- 
tial LS solution (Eq. 1), as in the 1994 
ICCAT assessment. The 2 dashed lines 
with symbols (virtually indistinguishable 
from each other) represent the final 
trimmed LS solutions, i.e. after removal 
of the outliers identified in Figure 4. Note 
that all the stock size estimates are iden- 
tical in the first half of the time series, 
owing to the convergence properties of the 
SPA. Differences in 1990’s stock size es- 
timates before and after trimming are 
most notable for small and medium blue- 
fin tuna (Fig. 5). For this example, the 
final trimmed LS solutions estimate 
lower current stock sizes (Fig. 5) and cor- 
respondingly higher current exploitation 
rates (not shown). 
The impact that these differences in the 
estimates have on management recom- 
mendations can be appreciated in Figure 
6, which shows a 10-year projection of the 
stock’s spawning biomass at two levels 
of constant landings considered by 
ICCAT. These projections were made by 
using the same assumptions as those in 
the assessment (Appendix BFTW-2 in 
ICCAT, 1995): essentially, that recruit- 
ment is constant after a certain parental 
biomass level and that the 3 most recent 
recruitment values from the SPA are 
poorly estimated and are replaced by the 
geometric mean recruitment from past 
years. The top panel in Figure 6 is a pro- 
jection made by assuming 2,000 metric 
tons (t) landings after 1993: the lower 
panel assumes 2,660 t landings after 
1993. The solid lines represent the LS 
solution as in the ICCAT assessment, and 
the dashed lines represent the LS solu- 
tions after trimming (squares for results 
from the LTSj solution and circles for re- 
sults from the LTS 2 solution). The pro- 
jections made without removing outliers 
Year 
Figure 5 
Bluefin tuna stock size estimates for 3 groups of ages. The solid line 
represents the estimates from the least-squares solution with all the 
available data, as in the ICCAT assessment. The dashed lines show the 
least squares estimates after removal of the data points identified as 
outliers in Figure 4. Squares = after minimization with Equation 2; circles 
= after minimization with Equation 3. Squares and circles overlap. 
