Chapter 3: Results
3.3
The annual biomass ratio (𝐵 𝐵𝑀𝑆𝑌) and fishing mortality ratio (𝐹 𝐹𝑀𝑆𝑌) of run
7 from 1952 - 2006 show in Fig. 4, and the explicit ratio of 𝐵2006 𝐵𝑀𝑆𝑌 and 𝐹2006 𝐹𝑀𝑆𝑌 in all base case and sensitive runs also show in Table 3.
23
In using equal weighting of all base case and sensitive runs, the estimated 𝐵2006 𝐵𝑀𝑆𝑌
ratio range between 0.61 and 0.90, and the estimated
𝐹2006 𝐹𝑀𝑆𝑌 ratiorange between 1.51 and 1.71. In using non-equal weighting of all base case and
sensitive runs, the estimated 𝐵2007 𝐵𝑀𝑆𝑌
ratio range between 0.25 and 2.05, and the
estimated 𝐹2006 𝐹𝑀𝑆𝑌
ratio range between 0.015 and 23.71.
3.4 Sensitive analysis
The results of sensitive analysis show in Table 3. When using equal weighting,
the results of MSY, K and FMSY are very similar; in non-equal weighting, the fitting
results quite different when using less fishery as CPUE indices such as using JPPS
and JPLL as baseline case run. Compared the fitting results of equal or non-equal
weighting, using non-equal weighting would obtain a lower MSY value in some base
case and sensitive runs. When using non-equal weighting, it could have lower AIC
value in the goodness of fit. When combining more CPUE indices into single index,
could not get better fitting results and there would be no solved in using single CPUE
index, such as: TWCOLL and JPPS CPUE only fitting model.
3.5 Projection
Run 7 is chosen to run the projection under different catch levels, due to run 7
24
converged with the smallest AIC value, and much more concentrated on B Bmsy
ratio and F Fmsy ratio in bootstrap analysis. Further, the different catch levels were
designed within the MSY ranges between 18,000 and 26,000 mt, those are 18,000 mt,
19,000 mt, 20,000 mt and 26,000 mt. The projected results of B Bmsy ratio show in
Fig. 7, and the results of F Fmsy ratio show in Fig. 8.
25
4. Discussion
The production model, also called surplus production model, have been used
widely in managing fisheries, largely because they are based only on catch and effort
data, which are relatively simple to collect. According to the techniques for model
fitting, it could be divided into equilibrium or non-equilibrium production models.
The equilibrium method depends on the assumption that catch rates are in equilibrium
with the natural production, this does not conform to relative situation, and is quiet
dangerous. On the contrary, the non-equilibrium production depends on the
assumption of process-error or observation-error methods (Hilborn & Walters, 1992;
Quinn & Deriso, 1999) in model fitting, and seems to be more reasonable than
equilibrium method. The generalized production model has a parameter, n, added to
the Schaefer logistic model, and could offer more flexibility in the shape of
productivity curves. This is the reason why this study just uses non-equilibrium
method and generalized production model for stock assessment of T. orientalis.
4.1 Generalized production model
This study is first application of generalized production modeling approach to
model the dynamics of Pacific bluefin tuna, assess the stock condition in relation to
biological reference point and project stock conditions in the future. MSY estimated
26
in this study range between 17,990 mt and 25,750 mt, was a little higher than Huang
in 2003 (5,676-24,563 mt). Multiple fishing methods in an area would estimate higher
MSY especially in purse seine and longline (Maunder, 2002), longline and purse seine
occupied great proportion of annual catch in Pacific bluefin tuna, and this might be
the reason why MSY estimated in this study is greater than Huang.
From fitting results in Table 3, using different CPUE index of fisheries as base
case and sensitive runs to fit generalized production model could get different trends
in MSY, K, 𝐹𝑀𝑆𝑌
,𝐵
𝑚𝑠𝑦n and phi. It is especially significant in using equal or
non-equal statistical weights of fisheries fit model. When using equal weighting, the fitting results of fishing mortality rate at MSY (𝐹𝑀𝑆𝑌) and MSY are similar in all base
case runs but are much more variable in non-equal weighting. This may be due to the
influence or the effect of statistical weight. In the annual catch of PBF in North
Pacific Ocean, purse seine fishery occupied more than 50% and using non-equal
statistical weight may enhance the property of fishing gears (high or low catchability),
tendency of CPUE or errors (bias) of datasets (years of datasets). The phi estimated
from all base case runs are smaller than 1 and according to Fletcher 1978, 𝛾 is
negative when n smaller than 1 and 𝛾 has a maximum value around 1. So 𝛾 is
negative in all base case runs.
4.2 𝐵 𝐵𝑀𝑆𝑌 and 𝐹 𝐹𝑀𝑆𝑌 ratio
27
In the historical trend of 𝐵 𝐵𝑀𝑆𝑌 and 𝐹 𝐹𝑀𝑆𝑌 ratio from 1952 to 2005, major
lay in fourth quadrant before 1980s, second quadrant after 1980s, first or fourth
quadrant after 1990s, and recent year was all in second quadrant. This present the
situation of the pacific bluefin tuna stock was overfished and overfishing after 1980s,
stock biomass restored in 1990s, overfishing and overfished in recent years.
𝐵2006 𝐵𝑀𝑆𝑌 ratio is lower than 1 or closer to 1, this shows that stock biomass of
T.orientalis was risky, and had tendency of overfished in 2006. The
𝐹2006 𝐹𝑀𝑆𝑌 ratiowas greater than 1, and this shows that fishing pressure for T.orientalis in North
Pacific Ocean was too high and had tendency of overfishing in 2006.
Comparing estimated biomass of Pacific bluefin tuna in this study (Fig. 9) with
VPA, which was made by Yamada in 2004, the tendency was similar in 1960s, 1980s,
1990s, and 2000s. There was a great difference in 1970s, the biomass had increased
trend in VPA, but in this study had decreased trend. This difference caused different
biomass level in recent years, the biomass was in good condition in VPA, but was in a
quite lower level in this study.
4.3 Sensitive analysis
In the application of production model, CPUE index is taken as abundance index
of stock biomass, and apply in model fitting. Hence, the accuracy and precision of
28
CPUE index is quite important. In this study, the unit of JPPS CPUE index is
unknown, and this might raise the uncertainty in model fitting. From the results of
sensitive analysis, using more CPUE index of fisheries as datasets would increase the
variation of fitting results, and using equal or non-equal statistical weight of fisheries
in model fitting also have influence in fitting results. Comparing the results of
sensitive analysis in using equal or non-equal weighting, using equal weighting are
much more stable than using non-equal weighting, but seems to be less sensitive. This
may be due to statistic weights are in good measurement of characteristics in different
fishery. In using non-equal weighting, adding Taiwan data into base case change the
fitting results a lot in some base case runs, and this may be due to Taiwan longline
fishery mainly target largest fish of PBF or Taiwan CPUE data only had 9 year CPUE
indices hence influencing the fitting results.
In combining CPUE indices, combined CPUE index of longline fishery could
have better fitting results (lower AIC) than combined CPUE index of purse seine
fishery. This might be due to estimating or standardizing CPUE index of purse seine
fishery is very difficult and fairly complicated. So combining different CPUE index of
purse seine fishery might cause much more errors or bias in model fitting. The unit of
Japanese purse seine CPUE index is unknown and this might increase uncertainty in
combining purse seine indices.
29
When using single CPUE index such as JPPS, JPTL and TWCOLL fit model,
there would be no fitting results. This might be due to the time series of these CPUE
index is too short and could not offer enough abundance index information in model
fitting.
4.4 Projection
Industrialized fisheries typically reduced community biomass by 80% within 15
years of exploitation (Myers, 2003), and Pacific bluefin tuna has already been
exploited over 50 years in North Pacific Ocean. It is quite important to understand
stock status and manage the fishery in North Pacific Ocean.
When using a higher quota (greater than 18,000 MT) as TAC for projection, the B Bmsy ratio will be less than 1 in 2022 and almost closer to zero. The F Fmsy ratio
will be larger than 1 and almost greater more than Fmsy four to six times. On the
contrary, when using a lower quota (smaller than 18,000 MT), the B Bmsy ratio will
be greater than 1 and biomass would be almost twice of Bmsy. The F Fmsy ratio will
be less than 1 and almost to half. From the results of projection, on purpose of making
sustainable exploitation of T. orientalis in North Pacific Ocean advice setting the
annual catch of T. orientalis in North Pacific Ocean to a lower than 18,000 mt.
30
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Myers, R. A. and Worm, B. 2003. Rapid worldwide depletion of predatory fish communities. Nature 425, 280-283.
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33
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Laboratory 25, 1-28.34
Table 1. Catches for Pacific bluefin tuna from 1952 to 2006.
Unit: Metric ton
Year
Western Pacific
Japan Korea Taiwan
Purse Seine Dist&Off LL
Coastal
Driftnet Others Sub total tuna PS small
35
Purse Seine Dist&Off LL
Coastal
Driftnet Others Sub total tuna PS small PS north
36
37
Table 2. Input parameters and CPUE indices for all base case and sensitive runs in ASPIC.
Model, parameter Base case Sensitive analysis Sensitive analysis Sensitive analysis
Run number Run 1 Run 2 Run 3 Run4
run data name a1 b1 b2 b3
Model of operation Fit Fit Fit Fit
Comment 'Pella and Tomlinson' 'Pella and Tomlinson' 'Pella and Tomlinson' 'Pella and Tomlinson'
Error type GENGRID YLD SSE 25 80 3 8.0 GENGRID YLD SSE 25 80 3 8.0 GENGRID YLD SSE 25 80 3 8.0 GENGRID YLD SSE 25 80 3 8.0
Verbosity 2 12 2 12 2 12 2 12
Number of bootstrap trials 0 0 0 0
Monte Carlo searching 1 50000 1 50000 1 50000 1 50000
Convergence criterion for optimizer 1.0d-8 1.0d-8 1.0d-8 1.0d-8
Restart control 3d-8 6 3d-8 6 3d-8 6 3d-8 6
Control of iterative computations 1d-6 16 1d-6 16 1d-6 16 1d-6 16
Maximum estimated F 8d0 8d0 8d0 8d0
Statistical weight for B1 penalty in objective function 0d0 0d0 0d0 0d0
Number of data series 3 3 4 4
Random number seed 1963285 1963285 1963285 1963285
Number of years in data set 55 55 55 55
Title CC CC CC CC
Data series PBF CPUE, Yield PBF CPUE, Yield PBF CPUE, Yield PBF CPUE, Yield
CPUE(s) used JPPS+JPLL+JPTL JPPS+JPLL+JPTL JPPS+JPLL+JPTL+TWCOLL JPPS+JPLL+JPTL+TWCOLL
38
Table 2. (continued).
Model, parameter Sensitive analysis g Sensitive analysis Sensitive analysis Sensitive analysis
Run number Run 5 Run 6 Run 7 Run 8
run data name b4 b5 b6 b7
Model of operation Fit Fit Fit Fit
Comment 'Pella and Tomlinson' 'Pella and Tomlinson' 'Pella and Tomlinson' 'Pella and Tomlinson'
Error type GENGRID YLD SSE 25 80 3 8.0 GENGRID YLD SSE 25 80 3 8.0 GENGRID YLD SSE 25 80 3 8.0 GENGRID YLD SSE 25 80 3 8.0
Verbosity 2 12 2 12 2 12 2 12
Number of bootstrap trials 0 0 0 0
Monte Carlo searching 1 50000 1 50000 1 50000 1 50000
Convergence criterion for optimizer 1.0d-8 1.0d-8 1.0d-8 1.0d-8
Restart control 3d-8 6 3d-8 6 3d-8 6 3d-8 6
Control of iterative computations 1d-6 16 1d-6 16 1d-6 16 1d-6 16
Maximum estimated F 8d0 8d0 8d0 8d0
Statistical weight for B1 penalty in objective function 0d0 0d0 0d0 0d0
Number of data series 5 3 3 4
Random number seed 1963285 1963285 1963285 1963285
Number of years in data set 55 55 55 55
Title CC CC CC CC
Data series PBF CPUE, Yield PBF CPUE, Yield PBF CPUE, Yield PBF CPUE, Yield
CPUE(s) used JPPS+JPLL+JPTL+TWCOLL+EPOPS EPOPS+JPLL+JPTL EPOPS+JPLL+JPTL EPOPS+JPLL+JPTL+TWCOLL
39
Table 2. (continued).
Model, parameter Sensitive analysis Sensitive analysis Sensitive analysis Sensitive analysis
Run number Run 9 Run 10 Run 11 Run 12
run data name b8 b9 b10 b11
Model of operation Fit Fit Fit Fit
Comment 'Pella and Tomlinson' 'Pella and Tomlinson' 'Pella and Tomlinson' 'Pella and Tomlinson'
Error type GENGRID YLD SSE 25 80 3
8.0 GENGRID YLD SSE 25 80 3 8.0 GENGRID YLD SSE 25 80 3 8.0 GENGRID YLD SSE 25 80 3 8.0
Verbosity 2 12 2 12 2 12 2 12
Number of bootstrap trials 0 0 0 0
Monte Carlo searching 1 50000 1 50000 1 50000 1 50000
Convergence criterion for optimizer 1.0d-8 1.0d-8 1.0d-8 1.0d-8
Restart control 3d-8 6 3d-8 6 3d-8 6 3d-8 6
Control of iterative computations 1d-6 16 1d-6 16 1d-6 16 1d-6 16
Maximum estimated F 8d0 8d0 8d0 8d0
Statistical weight for B1 penalty in objective function 0d0 0d0 0d0 0d0
Number of data series 4 3 3 6
Random number seed 1963285 1963285 1963285 1963285
Number of years in data set 55 55 55 55
Title CC CC CC CC
Data series PBF CPUE, Yield PBF CPUE, Yield PBF CPUE, Yield PBF CPUE, Yield
CPUE(s) used EPOPS+JPLL+JPTL+TWCOLL PCOPS, WESTLL, JPTL PCOPS, WESTLL, JPTL JPOFFLL, JPCOLL, EPOPS, JPTL, TWCOLL,
JPPS
40
Table 2. (continued).
Model, parameter Sensitive analysis Sensitive analysis Sensitive analysis Sensitive analysis
Run number Run 13 Run 14 Run 15 Run 16
run data name b12 b13 b14 b15
Model of operation Fit FIT FIT Fit
Comment 'Pella and Tomlinson' Pella and Tomlinson Pella and Tomlinson 'Pella and Tomlinson'
Error type GENGRID YLD SSE 25 80 3
8.0 GENGRID YLD SSE 25 80 3 8.0 GENGRID YLD SSE 25 80 3 8.0 GENGRID YLD SSE 25 80 3 8.0
Verbosity 2 12 2 12 2 12 2 12
Number of bootstrap trials 0 0 0 0
Monte Carlo searching 1 50000 1 50000 1 50000 1 50000
Convergence criterion for optimizer 1.0d-8 1.0d-8 1.0d-8 1.0d-8
Restart control 3d-8 6 3d-8 6 3d-8 6 3d-8 6
Control of iterative computations 1d-6 16 1d-6 16 1d-6 16 1d-6 16
Maximum estimated F 8d0 8d0 8d0 8d0
Statistical weight for B1 penalty in objective function 0d0 1d0 1d0 0d0
Number of data series 6 1 1 4
Series-specific statistical weights 2.4d-1 0.5d-1 0.6d-1 0.9d-1
0.2d-1 5.4d-1 1 1 1 1 1 1
Random number seed 1963285 1963285 1963285 1963285
Number of years in data set 55 55 55 55
Title CC CC CC CC
Data series PBF CPUE, Yield PBF CPUE, Yield PBF CPUE, Yield PBF CPUE, Yield
CPUE(s) used JPOFFLL, JPCOLL, EPOPS, JPTL, TWCOLL, JPPS
TWCOLL CPUE only JPPS CPUE only WESTLL, EPOPS, JPTL, JPPS
41
Table 2. (continued).
Model, parameter Sensitive analysis Sensitive analysis Sensitive analysis Sensitive analysis
Run number Run 17 Run 18 Run 19 Run 20
run data name b16 b17 b18 b19
Model of operation Fit FIT FIT Fit
Comment 'Pella and Tomlinson' Pella and Tomlinson Pella and Tomlinson 'Pella and Tomlinson'
Error type GENGRID YLD SSE 25 80 3 8.0 GENGRID YLD SSE 25 80 3 8.0 GENGRID YLD SSE 25 80 3 8.0 GENGRID YLD SSE 25 80 3 8.0
Verbosity 2 12 2 12 2 12 2 12
Number of bootstrap trials 0 0 0 0
Monte Carlo searching 1 50000 1 50000 1 50000 1 50000
Convergence criterion for optimizer 1.0d-8 1.0d-8 1.0d-8 1.0d-8
Restart control 3d-8 6 3d-8 6 3d-8 6 3d-8 6
Control of iterative computations 1d-6 16 1d-6 16 1d-6 16 1d-6 16
Maximum estimated F 8d0 8d0 8d0 8d0
Statistical weight for B1 penalty in objective function 0d0 0d0 0d0 0d0
Number of data series 4 2 2 5
Random number seed 1963285 1963285 1963285 1963285
Number of years in data set 55 55 55 55
Title CC CC CC CC
Data series PBF CPUE, Yield PBF CPUE, Yield PBF CPUE, Yield PBF CPUE, Yield
CPUE(s) used WESTLL, EPOPS, JPTL, JPPS JPLL, EPOPS JPLL, EPOPS JPPS+JPLL+JPTL+TWCOLL+EPOPS
42
Table 3. Results of the ASPIC potential base case and sensitive runs. MSY: maximum sustainable yield; 𝐹𝑀𝑆𝑌: fishing mortality give MSY;
𝑓𝑀𝑆𝑌: fishing effort of each fishery in MSY; 𝐵𝑀𝑆𝑌: biomass giving MSY; 𝛾: Fletcher's gamma; K: maximum population size; 𝑞:
catchability of each fishery; n: exponent in production function.
Model,
parameter Base case Sensitive
analysis Sensitive
Model
GENGRID GENGRID GENGRID GENGRIDGENGRID GENGRID GENGRID GENGRID
Year of data
1952-2006 1952-2006 1952-2006 1952-2006 1952-2006 1952-2006 1952-2006 1952-2006
CPUE(s)
equal non-equal equal non-equal equal equal non-equal equal
MSY (MT) 17990 24240 25750
43
Model
GENGRIDGENGRID
GENGRIDGENGRID GENGRID GENGRID GENGRID
Year of data
1952-2006 1952-2006 1952-2006 1952-2006 1952-2006 1952-2006 1952-2006
CPUE(s) used
EPOPS+JPLL+JPTL+TWCOLL PCOPS, WESTLL, JPTL PCOPS, WESTLL, JPTL JPOFFLL, JPCOLL, EPOPS, JPTL, TWCOLL,
JPPS
JPOFFLL, JPCOLL, EPOPS, JPTL, TWCOLL,
JPPS
TWCOLL CPUE only JPPS CPUE only
Weighting
No con verge d No co nver ge d No con verge d No con verge d
K (MT) 256600 15530000
44
Model
GENGRID GENGRID GENGRID GENGRID GENGRIDYear of data
1952-2006 1952-2006 1952-2006 1952-2006 1952-2006
CPUE(s)
JPLL, EPOPS JPLL, EPOPS JPPS+JPLL+JPTL+TWCOLL+EPOPS
Weighting of fishery
equal non-equal equal non-equal non-equal
MSY (MT)
45
Table 4. Detailed fitting results and estimated model parameters in sensitive run 7.
46
Table 4. (continued).
47
Fig.1. The annual catches of pacific bluefin tuna from 1950 to 2005 (Data sources:
Anon,, 2007).
0 5 10 15 20 25 30 35 40 45
1952 1957 1962 1967 1972 1977 1982 1987 1992 1997 2002
Ca tch (10 00 metric ton s)
Year
EPOPS JPLL JPTL TWCOLL JPPS
2007
48
Fig. 2. Main fishery targets for Pacific bluefin tuna in Northern Pacific.
Longline Purse seine Troll
Set net Pole and line
49
(a)
(b)
(c)
(d)
Fig. 3. The estimated time series of CPUE from each data source.(a) Japan longline offshore (b) Japan longline coastal (c) Taiwan longline (d) Eastern Pacific Ocean purse seine (e) Japan purse seine (f) Japan troll.
0 1 2
1952 1962 1972 1982 1992 2002
CPUE
1952 1962 1972 1982 1992 2002
CPUE
1952 1962 1972 1982 1992 2002
CPUE
1952 1962 1972 1982 1992 2002
CPUE
Year
EPO purse seine
50
1952 1962 1972 1982 1992 2002
CPUE
1952 1962 1972 1982 1992 2002
CPUE
Year Japan troll
51
(a)
(b)
Fig. 4. Detailed descriptions of re-arrangement fishery catch data in run 1 ~ run20 (a) run1 & run2 (b) run3 & run4 (c) run5 & run20 (d) run6 & run7 (e) run8 &
run9 (f) run10 & run11 (g ) run12 & run13 (h) run16 & run17 (i) run18 &
run19.
52
53
54
JPTL Japan Troll JPOFFLL Japan Dist&Off LL
55
56
Fig. 5. Annual biomass ratio (B BMSY) and fishing mortality ratio (F FMSY) ratio for Pacific bluefin tuna (1952-2006) using generalized production model in run 7.
0 1 2 3 4 5
57
(a)
Fig. 6. The fitting results of run 7 (EPOPS, JPLL, and JPTL)(non-equal).
(a)CPUE trajectory of each fishery (b) B-ratio and F-ratio (c) B-ratio and F-ratio of model and bootstrap (d)distribution of relationship between B-ratio and F-ratio in 2006.
58
(b)
(c)
Fig. 6. (continued).
59
(d)
Fig. 6. (continued).
60
(a)
(b)
Fig. 7. The results of using run 7 for projection in B Bmsy ratio after 15 year.
(a)catch level : 18,000 mt (b)catch level : 19,000 mt (c)catch level : 20,000 mt (d) catch level : 26,000 mt
61
(c)
(d)
Fig. 7. (continued).
62
(a)
(b)
Fig. 8. The results of using base case run 7 for projection in F Fmsy ratio after 15 year. (a)catch level : 18,000 mt (b)catch level : 19,000 mt (c)catch level : 20,000 mt(d) catch level : 26,000 mt
63
(c)
(d)
Fig. 8. (continued).
64
Fig. 9. The estimated average biomass of Pacific bluefin tuna in this study from 1952 to 2006.