_{1}

One error was found in the coding of the simulation program for reproducing the recruitment (R) and spawning stock biomass (SSB) of the Pacific stock of the Japanese sardine. As a result of this error, the maturity rate for age 1 in the simulation was found to be half of the value cited from the literature. The aim of this paper is to show the results when the error is corrected. When the error was corrected, the r eproduced R and SSB were slightly higher than the values shown in the previous paper. When the fishing mortality coeffcients (F) before 2003 and after 2004 were assumed to be 10% higher and 50% lower than the values cited, respectively, the results coincided better with R and SSB cited. The only difference between the simulation conducted in this paper and that conducted in the previous paper is the assumption that the value of F before 2003 was 10% higher than the values cited. Therefore, the effect of the error was not serious, and the essential conclusions noted in the previous paper did not change.

Among Japanese fisheries, the Japanese sardine (Sardinops melanostictus) is one of the most important species in the northwestern Pacific. In 1997, the Japanese Government introduced a total allowable catch (TAC) system for seven species including sardine. Sardine numbers began to increase during the 1960s and were very high in the 1980s, but decreased markedly in the early 1990s and have remained low. Since the TAC system was introduced, many fishermen who harvest sardine have opposed the schemes for management of the depleted populations. The government of Japan insists that a reduction in the TAC is necessary to rehabilitate the sardine population, but the fishermen insist that a reduction is not appropriate because the fluctuations in sardine population abundance are mainly caused by environmental factors. To establish management schemes that are acceptable to fishermen but meet government management objectives, fisheries scientists need new models of sardine population abundance that can explain the extremely large fluctuations in recruitment and the spawning stock biomass.

Sakuramoto proposed a new stock-recruitment relationship for the Pacific stock of the Japanese sardine [

ln ( R P S t ) = 15.713 − 0.108 A O t 2 − 0.0745 A O t 3 − 0.0011 K E S T t 3 + 0.0187 A O t × K E S T t (1)

where AO_{t} and KEST_{t} respectively denote the Arctic oscillation (AO) in February of year t and the sea surface temperature over the southern area of the Kuroshio Extension from 30˚N to 35˚N and 145˚E to 180˚E (KEST) in February. The natural logarithm of the recruitment per spawning stock biomass (RPS) is denoted by ln(RPS). Using Equation (1), R and SSB were reproduced provided that the numbers of fish by age in 1976 were given as the initial values and that environmental factors such as AO and KEST were known. The procedure by which R and SSB were reproduced was explained in detail in the previous paper [

In this study, I used values for the catch, average weight, maturity rate, and natural mortality coefficient, all of which are recorded by age and year, for the northwestern Pacific stock from 1976 to 2012 [

The simulation program was coded with MATLAB software Version R2013b. The incorrect sentence in the program is as follows:

Stcal ( t + 1 ) = Stcal ( t + 1 ) + mature ( t + 1 , a ) * SSBcal ( t + 1 , a ) , (2)

where Stcal (t + 1), mature (t + 1, a), and SSBcal (t + 1, a) denote the reproduced values of SSB in year t + 1, the maturity rate at age a in year t + 1, and the reproduced values of SSB at age a in year t + 1 (a = 0, 1,∙∙∙, 5 +), respectively. The line should be replaced by the following:

Stcal ( t + 1 ) = Stcal ( t + 1 ) + SSBcal ( t + 1 , a ) . (3)

That is, the maturity rate, mature(t + 1, a), in Equation (2) should be removed. As a result of this error, the maturity rate for age 1 was doubly multiplied. The maturity rate for age 0 is zero, and those for ages 2 and older are unity; therefore, the values calculated with Equations (2) and (3) are not different for ages 0 and for ages 2 and older. However, the maturity rate for age 1 cited is 0.5. When Equation (2) is used, the rate of matured fish at age 1 is wrongly calculated by multiplying 0.5 * 0.5 = 0.25 by the number of fish at the age of 1. That is, the calculated number of matured fish at age 1 was half of the true value. This caused the underestimation of R and SSB.

In the previous paper, the fishing mortality coefficients after 2004 were halved so as to minimize the differences between the values cited and reproduced of R and SSB after 2004, because the reproduced R and SSB were much smaller than those cited from the literature [

Scenario | F (1976-2003) | F (2004-2012) | M (1976-2003) | M (2004-2012) | Figure |
---|---|---|---|---|---|

1 | F | F | M | M | |

2 | F | 0.50 F | M | M | |

3 | 1.10 F | 0.50 F | M | M | |

4 | F | F | 1.05 M | 0.10 M |

of the value. In this case, the reproduced R after 2005 and SSB values after 2006 were larger than those in

This paper showed the results when the error in the program was corrected. There was a tendency for the reproduced R and SSB values before 2003 to be slightly large, and for those after 2005 to be much lower than the values cited. Three possibilities were considered as interpretations of this phenomenon. One is that actual F before 2003 was higher than the values cited and actual F after

2004 was lower than the values to be referred. When we assumed that F before 2003 was 10% higher than the values cited and F after 2004 was 50% lower than the values cited, the reproduced R and SSB values coincided well with those cited. The second possibility is that true M before 2003 was higher than the value cited and true M after 2004 was lower than the value cited. When we assumed that true M before 2003 was 5% higher than the value cited and true M after 2004 was 90% lower than the value cited, the reproduced R and SSB values coincided well with those cited. However, the latter assumption, in which M after 2004 was 10% of the value cited, was extremely low and was considered to be unrealistic. The third possibility is that the above two scenarios were combined. Although using an M value after 2004 that was 10% of the value cited was unrealistic, for the other scenarios we cannot determine which value was more realistic at this stage.

Although the aim of this study is not to find the best parameters that give the best fit to R and SSB cited, we could determine the best combination of F and M that minimize the differences between the values reproduced and cited of R and SSB. Other parameters, such as the mean weight of fish by age and the maturity rate by age, are also important. All of those parameters fluctuate year by year; therefore, if we can use the accurate values of F, M, the maturity rate by age, and the mean weight by age for each year, the fitting of the reproduced values to those cited would be much batter.

The same correction was conducted for the paper on Pacific bluefin tuna that was analyzed by Sakuramoto [

When the error in the program was corrected, the results did not change greatly from those obtained when the wrong program was used. When the value of F to be referred before 2003 was replaced by a value 10% higher than the value cited and the value of F after 2004 was replaced with 50% of the value cited, the reproduced R and SSB values coincided well with those cited. Therefore, the effect of the error was not serious, and the essential conclusions noted in the previous paper did not change.

I would like to thank KN International for improving the manuscript.

Sakuramoto, K. (2017) Correction of “A Recruitment Fore- casting Model for the Pacific Stock of the Japanese Sardine (Sardinops melanostictus) That Does Not Assume Density-Dependent Effects”. Open Access Library Journal, 4: e3620. https://doi.org/10.4236/oalib.1103620