This study proposes a simulation model that well reproduces the spawning stock biomass of Pacific bluefin tuna. Environmental factors were chosen to estimate the recruitment per spawning stock biomass, and a simulation model that well reproduced the spawning stock biomass was developed. Then, effects of various fisheries regulations were evaluated using the simulation study. The results were as follows: 1) arctic oscillations, Pacific decadal oscillations and the recruitment number of the Pacific stock of Japanese sardine were chosen as the environmental factors that determined the recruitment per spawning stock biomass; 2) spawning stock biomass could be well reproduced using a model that reproduced the recruitment per spawning stock biomass and the survival process of the population that included the effect of fishing; and 3) the effects of various fisheries regulation could be evaluated using the simulation model mentioned above. The effective regulation in the simulations conducted in this paper was a prohibition of fishing for 0- and 1-year-old fish in terms of recovering the spawning stock biomass. The reduction of fishing mortality coefficients for all age fish to 50% of actual values also showed a good performance. The recent reductions of the recruitment and spawning stock biomass were likely caused by heavy harvesting, especially of immature fish, since 2004.
The abundance of Pacific bluefin tuna, Thunnus thynnus, has seriously decreased in recent years. In 1952, the starting year of the current stock assessment, total stock biomass was 119,400 t. During the stock assessment period, the total stock biomass reached the historical maximum of 185,559 t in 1959, and a historical minimum of 40,263 t in 1983. Total stock biomass started to increase again in the mid-1980s and reached its second highest peak of 123,286 t in 1995. Total stock biomass decreased throughout 2008-2012, averaging 50,243 t per year, but reached 44,848 t in 2012 [
Recently, however, Sakuramoto [
where Rt and St-1 denote the recruitment in year t and spawning stock biomass in year t-1, respectively. The f(.) denotes a function that evaluates the effects of environmental factors in year t. The variable
The purpose of this study is to investigate whether or not the SRR model described by equation (1) is applicable to Pacific bluefin tuna, and can reproduce the trajectory of SSB. Another aim of this study is to evaluate the effect on SSB of fisheries regulations for Pacific bluefin tuna using the simulation model developed in this study.
The data used in this study are as follows: 1) Recruitment of Pacific bluefin tuna, derived from the report of the International Scientific Committee (ISC) [
where 0.25 is the natural mortality coefficient for ≥10-year-old fish. Otherwise, the average weights by age were calculated using the growth curve and length-weight relationship used in the ISC [
All the data used in this study can be easily obtained through the internet. However, Sakuramoto [
where M is 0.4, which is the natural mortality coefficient for the Pacific stock of Japanese sardine for age 0, and Ft,0 denotes the fishing mortality coefficient for the Pacific stock of Japanese sardine for age 0 in year t. The average of dift was 1.826, which corresponded to 6% - 9% of the observed
As the environmental conditions, AO in month m of year t,
The procedure to reproduce SSB is shown in
Step 1: The initial values of population at age a in year 1953,
Step 2: SSB in year t,
where ma and wa denote the maturity rate and mean weight at age a.
Year | lnR | Year | lnR | Year | lnR |
---|---|---|---|---|---|
1953 | 7.232 | 1973 | 11.170 | 1993 | 9.403 |
1954 | 6.872 | 1974 | 9.278 | 1994 | 9.383 |
1955 | 6.691 | 1975 | 10.145 | 1995 | 8.897 |
1956 | 6.545 | 1976 | 10.931 | 1996 | 9.506 |
1957 | 6.736 | 1977 | 11.432 | 1997 | 8.958 |
1958 | 8.229 | 1978 | 11.453 | 1998 | 8.906 |
1959 | 8.548 | 1979 | 10.644 | 1999 | 7.844 |
1960 | 6.807 | 1980 | 12.588 | 2000 | 8.477 |
1961 | 6.412 | 1981 | 12.195 | 2001 | 8.414* |
1962 | 6.103 | 1982 | 11.959 | 2002 | 7.687* |
1963 | 5.652 | 1983 | 12.102 | 2003 | 7.592* |
1964 | 5.153 | 1984 | 12.268 | 2004 | 7.352* |
1965 | 4.963 | 1985 | 12.421 | 2005 | 8.338* |
1966 | 5.136 | 1986 | 12.468 | 2006 | 7.903* |
1967 | 5.380 | 1987 | 11.961 | 2007 | 7.994* |
1968 | 5.649 | 1988 | 10.037 | 2008 | 8.501* |
1969 | 6.180 | 1989 | 9.875 | 2009 | 8.149* |
1970 | 7.363 | 1990 | 8.843 | 2010 | 9.919* |
1971 | 9.133 | 1991 | 8.577 | 2011 | 9.125* |
1972 | 7.462 | 1992 | 10.216 | 2012 | 9.776* |
Step 3: The number of individuals at age a in the next year t + 1 (1 ≤ a ≤ 10+, 1953 ≤ t ≤ 2011),
Step 4: Recruitment in the next year t + 1 (1953 ≤ t ≤ 2011) is calculated using the following equation:
Here,
Step 5: Catch at age a (0 ≤ a ≤ 10+) in year t + 1 (1952 ≤ t ≤ 2011) is calculated using the following equation:
The effects of fisheries regulations were evaluated using simulation studies. As we show the trajectory of SSB later, the SSB was very low in the middle of 1980s. Then we assumed that a regulation was commenced for 5 years from 1987 to 1991 (
Scenario A1 is the case when all the fishing mortality coefficients for age 0 to (10+)-year-old fish were reduced to 50% of the actual values. Scenario A2 is the case in which fishing for age 0- and 1-year-old fish was prohibited. That is, the fishing mortality coefficients for 0- and 1-year-old fish were set at zero in the simulation. Scenario A3 is the case when fishing mortality coefficients for 0- to 3-year-old fish were reduced to 50% of the actual values. Scenario A4 is the case when fishing the only prohibition was against catching fish less than 1 year old.
The effect of the regulation for SSB in year t, ESt, is evaluated using the following equations:
Scenario | fisheries regulations | Year | Age | F values |
---|---|---|---|---|
A1 | Regulation for all age | 1987-1991 | 0 - 10+ | Fa,reg = 0.5 Fa, ISC, (a = 0, 1, 2, …, 10+) |
A2 | Regulation for juvenile | 1987-1991 | 0 - 1 | Fa, reg = 0.0, (a = 0 and 1) |
A3 | Regulation for juvenile | 1987-1991 | 0 - 3 | Fa, reg = 0.5 Fa, ISC (a = 0, 1, 2, and 3) |
A4 | Regulation for juvenile | 1987-1991 | 0 | F0, reg = 0.0 |
B1 | Regulation for all age | 2004-2012 | 0 - 10+ | Fa, reg = 0.5 Fa, ISC, (a = 0, 1, 2, …, 10+) |
B2 | Regulation for juvenile | 2004-2012 | 0 - 1 | Fa, reg = 0.0, (a = 0 and 1) |
B3 | Regulation for juvenile | 2004-2012 | 0 - 3 | Fa, reg = 0.5 Fa, ISC, (a = 0, 1, 2, and 3) |
B4 | Regulation for juvenile | 2004-2012 | 0 | F0, reg = 0.0 |
Here,
The effect of the regulation for catch in year t, ECt, is evaluated using the following equations:
Here,
In order to evaluate the cause of the recent reduction of R and SSB, simulations were conducted on the fisheries regulations that commenced from 2004 to 2012 (
The following model was selected by the stepwise method, which made the AIC being the minimum (AIC = −68.00)
where the figures in the suffixes for A and P denote the month in AO and PDO, respectively. The RSardine, t denotes the recruitment of the Pacific stock of Japanese sardine in year t. The RPS reproduced by this model, which was transformed from ln (RPS), is shown in
However, for the other years, the reproduced and observed RPSs coincided well.
We conducted sensitivity tests on models intended to reproduces ln (RPS) and ln (R), respectively.
Simulations were commenced according to the process shown in
Then Ma values were replaced by 0.9772 × Ma (
Model | Dependent variable | Factors used as the candidates to check by stepwise method | Factors chosen by stepwise method | AIC |
---|---|---|---|---|
1 | ln (RPS) | AO, PDO | A2, A3, A4, A7, P3, P4, P9, P10 | −45.1 |
2 | ln (RPS) | AO, PDO, Rsardine (ref), SSBsardine (ref) | A2, A3, A4, A6, A7, P4, P9, P10, Rsardine (ref) | −63.75 |
3 | ln (RPS) | AO, PDO, Rsardine, SSBsardine | A2, A3, A4, A6, A7, P4, P9, P10, Rsardine | −68.00 |
4 | ln (RPS) | AO, PDO, SSBbluefin | A1, A3, A6, P3, P4, P6, P7, P9, P10, SSBbluefin | −92.45 |
5 | ln (RPS) | AO, PDO, Rsardine, SSBsardine, SSBbluefin | A1, A2, A6, P4, P6, P7, P9, P10, Rsardine, SSBbluefin | −93.03 |
6 | ln (RPS) | AO, PDO, R of sardine, SSBsardine, Rbluefin | A2, A3, A4, A7, A9, P5, P9, Rsardine, Rbluefin | −116.38 |
7 | ln (RPS) | AO, PDO, Rsardine, SSBsardine, SSBbluefin, Rbluefin | A3, A8, Rbluefin, SSBbluefin | −2364.98 |
8 | ln (R) | AO, PDO, Rsardine, SSBsardine, SSBbluefin | A2, A3, A6, P4, P6, P7, P9, P10, Rsardine | −93.96 |
9 | ln (R) | AO, PDO | A1, A3, A6, P3, P4, P6, P9, P10 | −94.44 |
first couple of years, the amount of catch decreased; however, after that, the catch steeply increased, and in 1997 catch exceeded more than 80% larger than that when no regulation was present (scenario A2). The effects were the same of that shown in the SSB; that is, scenario A2 was the most effective regulation and next was scenario A1.
One innovative approach of this study was to reproduce the RPS only by using the environmental factors and the biological relationship. That is, RPS was reproduced using the AO in February, March, April, June, and July, and PDO in April, September, and October. It is considered that the AO and PDO play an important role in determining the environmental conditions over the spawning areas and adjacent areas where juvenile fish migrate.
The recruitment number of Japanese sardine was also an important factor for reproducing the RPS. Several possible reasons can be considered. One is that the high recruitment of Japanese sardine indicates that the environmental conditions that year were good for Japanese sardine; for instance, the amounts of the type of planktons that sardines feed on were abundant. Those environmental conditions might be also good for Pacific bluefin tuna. That is, the recruitment level of Japanese sardine could be used as an index that evaluates the goodness of the environmental conditions for Pacific bluefin tuna. Another is that the high recruitment of Japanese sardine itself is a good feeding condition for juvenile bluefin tuna, etc. Although it is difficult to clearly elucidate the direct biological reasons, this paper is the first to attempt to incorporate a biological relationship into the RPS for Pacific bluefin tuna, and this may also provide some insight into elucidating the mechanism in SRR.
The sensitivity tests shown in
cases when ln (RPS) was used as the dependent variable. When monthly AO and PDO were only used, i.e., the 24 variables were used as the candidates of environmental factors (Model 1), the selected variables were AO in February, March, April and July, and PDO in March, April, September and October, and the AIC value was −45.10, of which the fitness between the SSB reproduced by the model and the reference value was not good. When the R and SSB of the Japanese sardine were incorporated into the candidate environmental factors (Model 2), the R of the Japanese sardine was added as a variable of the optimal model, and the value of AIC became much smaller (AIC = −63.75). Further, when the modified recruitment of Japanese sardine was used (Model 3), the value of AIC was further improved (AIC = −68.00).
On the contrary, when the SSB of Pacific bluefin tuna was incorporated into the candidate factors (Model 4 or
5), regardless of whether the R of the Japanese sardine was incorporated or not, the value of AIC became much smaller (AIC = −92.5 or −93.03). Some scientists may consider that this provides clear evidence that a density-dependent effect exists. However, this is really just the illusion of a density-dependent effect. A density-dependent effect can easily explain the important phenomena observed in the population fluctuations; however, it is not a valid explanation as described in detail in the following section.
It is worth emphasizing that when the ln (R) of bluefin tuna was added to the candidate factors instead of ln (SSB) of bluefin tuna (Model 6), the ln (R) of bluefin tuna was chosen as the factor of the optimal model and the resultant optimal model showed much smaller AIC (AIC = −116.38) than that of Model 4 or 5. Therefore, Model 6, which is the model that assumes a positive density-dependent effect by ln (R), was much better than Model 5, which is the usual model to assume a negative density-dependent effect by ln (SSB). However, it does not make sense because the results only indicate that ln (SSB) has a negative relationship to ln (RPS); i.e., ln (SSB) exists in the denominator in ln (RPS), and ln (R) has a positive relationship to ln (RPS); i.e., ln (R) exists in the numerator in ln (RPS). Therefore, when ln (SSB) or ln (R) was added as a candidate factor, the resultant AIC value greatly decreased whether or not the model was valid.
Generally, the same variable in the left side of the equation should not appear in the right-hand side of the same equation. When both the ln (R) and ln (SSB) of bluefin tuna were added as candidate factors (Model 7), both variables were selected as the variables that constructed the optimal model, and the AIC of the resultant optimal model became extremely low (AIC = −2364.98). When this model was applied, the reference and reproduced ln (RPS) values completely coincided with each other. However, the results are a matter of course, because the same values in the left-hand side were used in the right-hand side in equation (11). That is, the minimum AIC does not always indicate a valid model and does not show the validity of the existing of density-dependent effect [
The last two models in
ln (SSB) was detected.
Model 9 was conducted to compare the result of Model 8; i.e., only AO by month and PDO by month were used as candidate factors. In this case, AIC was slightly large compared to Model 8. That is, the ln (R) of bluefin tuna can be well explained only by environmental factors (see
Here, a serious question emerges: namely, which model should we accept as the reasonable model to explain the fluctuation of recruitment? One model uses ln (R) as the dependent variable and the other uses ln (RPS) as the dependent variable. A detailed discussion of this question has already been published by Sakuramoto [
In this study, only AO and PDO were used as the physical environmental factors, and R and SSB of the Pacific stock of Japanese sardine were used as biological environmental factors. Other data such as a water temperature over the spawning area and adjacent area, and other indices of physical environmental factors should also be tested as candidate environmental factors.
In this study, the modified recruitment for the Pacific stock of Japanese sardine was used. If reference values of recruitment for the Pacific stock of Japanese sardine were used, the AIC value was little larger (AIC = −63.75) than the case when the modified value was used (AIC = −68.00) as shown in
The simulation model that reproduced the R, SSB and catch was extremely sensitive to the given values of natural mortality coefficient, fishing mortality coefficient, mean weight by age and maturity rate by age. As shown in this paper, a slightly smaller natural mortality coefficient reproduced the SSB trends well. However, not only the natural mortality coefficient but also the mean weight by age and maturity rate by age must change year by year. If those detailed and precise information could be made available, the reproduced SSB and catch
Period of regulation | The most effective scenario |
---|---|
1982-1986 | Scenario A1 |
1983-1987 | Scenario A1 |
1984-1988 | Scenario A1 |
1985-1989 | Scenario A1 |
1986-1990 | Scenario A2 |
1987-1991 | Scenario A2 |
1988-1992 | Scenario A2 |
1989-1993 | Scenario A2 |
1990-1994 | Scenario A2 |
1991-1995 | Scenario A2 |
will explain the fluctuation of the actual ones much better.
In the simulations conducted in this study, the most effective regulation was scenario A2. That is, the effect of the prohibition on age 0 and 1-year-old fishing showed the best performance for recovering the SSB and R. This is because, for Pacific bluefin tuna, the catch number for age 0- and 1-year-old fish has been extremely high (
The price for age 0- and 1-year-old fish is low; therefore, regulations to protect juvenile fish might have economic as well as biological merit. However, there are many coastal fishermen who harvest the immature fish of this bluefin tuna. Therefore, when scenario A2 or B2 is chosen for the recovery of this stock, we should carefully consider the effect of the regulation for those fishermen.
1) Recruitment per spawning stock biomass of Pacific bluefin tuna can be reproduced using the Arctic Oscillation by month, Pacific decadal oscillation by month and the recruitment number of the Pacific stock of Japanese sardine.
2) Spawning stock biomass could be well reproduced using the simulation model that was constructed with the recruitment per spawning stock biomass and the survival process of population that included the effect of fishing.
3) The effective regulation in the simulations conducted in this paper was a prohibition of fishing for 0- and 1-year-old fish in terms of recovering the spawning stock biomass. The reduction of fishing mortality coefficients for all age fish to 50% of actual values also showed a good performance.
4) The recent reductions of the recruitment and spawning stock biomass appear to be caused by the unregulated harvests, especially for immature fish, since 2004.
I thank the Fisheries Agency and Fisheries Research Agency of Japan for providing the recruitment and spawning stock biomass data for the Pacific stock of Japanese sardine. I also thank Drs. Jiro Suzuki, Tokio Wada, Takashi Koya, Naoki Suzuki and Rikio Sato for their useful comments that improved this manuscript.
Kazumi Sakuramoto, (2016) Case Study: A Simulation Model of the Spawning Stock Biomass of Pacific Bluefin Tuna and Evaluation of Fisheries Regulations. American Journal of Climate Change,05,245-260. doi: 10.4236/ajcc.2016.52021