# Assessment and Management of Small Yellow Croaker (Larimichthys polyactis) Stocks in South Korea

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data

#### 2.2. Generalized Linear Model for CPUE Standardization

#### 2.3. Surplus Production Model

#### 2.4. Bayesian State-Space Model

#### Model Implementation and Comparison

## 3. Results

#### 3.1. GLM Analysis Results and Model Comparison

^{2}value of the estimate was very high, at 0.99. As illustrated in Figure 5, all standardized CPUEs were included in the posterior 95% confidence level of the CPUE estimated using the Bayesian state-space model. Therefore, small yellow croaker stocks were assessed based on the estimates of the Bayesian state-space model, with an inverse-gamma distribution, using the Fox model, which has the lowest DIC.

_{MSY}) (56,985 tons). However, since 1992, its biomass has exhibited considerable variations, and it had dropped below the B

_{MSY}between 1993 and 2004.

_{MSY}.

#### 3.2. Analysis of Appropriate TAC Levels

_{1.2}), 10% increase (TAC

_{1.1}), 10% decrease (TAC

_{0.9}), 20% decrease (TAC

_{0.8}), and 20,800 tons (TAC

_{1.0}), which was the mean catch of small yellow croakers by gill-net, stow-net, and pair-trawl fisheries in 2014–2018, and the MSY (TAC

_{MSY}) of 21,301 tons.

## 4. Discussion

_{MSY}, which was substantially different from the results obtained with the Fox function, where the biomass was greater than the B

_{MSY}. The sensitivity analysis for the Bayesian state-space model estimates to date has focused on prior distributions. However, in future Bayesian state-space model estimates, more reliable stock assessments could be obtained if growth function analyses are performed in addition to sensitivity analysis for prior distributions.

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

Variable | Coefficient | Std. Error | t-Statistics | p-Value |
---|---|---|---|---|

(Intercept) | 0.294 | 0.316 | 0.931 | 0.357 |

year1993 | −0.042 | 0.4 | −0.106 | 0.916 |

year1994 | 0.072 | 0.4 | 0.179 | 0.858 |

year1995 | −0.069 | 0.4 | −0.172 | 0.865 |

year1996 | −0.153 | 0.4 | −0.383 | 0.703 |

year1997 | −0.208 | 0.4 | −0.52 | 0.605 |

year1998 | −0.444 | 0.4 | −1.112 | 0.272 |

year1999 | −0.377 | 0.4 | −0.944 | 0.350 |

year2000 | 1.818 | 0.46 | 3.952 | 0.000 *** |

year2001 | 0.836 | 0.46 | 1.817 | 0.076 . |

year2002 | 1.496 | 0.46 | 3.252 | 0.002 ** |

year2003 | 1.17 | 0.46 | 2.543 | 0.014 * |

year2004 | 2.145 | 0.46 | 4.663 | 0.000 *** |

year2005 | 2.724 | 0.437 | 6.231 | 0.000 *** |

year2006 | 3.272 | 0.437 | 7.484 | 0.000 *** |

year2007 | 3.769 | 0.437 | 8.619 | 0.000 *** |

year2008 | 3.631 | 0.437 | 8.305 | 0.000 *** |

year2009 | 3.761 | 0.437 | 8.603 | 0.000 *** |

year2010 | 3.549 | 0.437 | 8.118 | 0.000 *** |

year2011 | 4.547 | 0.437 | 10.399 | 0.000 *** |

year2012 | 3.855 | 0.437 | 8.818 | 0.000 *** |

year2013 | 3.516 | 0.437 | 8.043 | 0.000 *** |

year2014 | 3.448 | 0.437 | 7.886 | 0.000 *** |

year2015 | 3.658 | 0.437 | 8.367 | 0.000 *** |

year2016 | 2.76 | 0.437 | 6.312 | 0.000 *** |

year2017 | 2.638 | 0.437 | 6.034 | 0.000 *** |

year2018 | 2.752 | 0.437 | 6.294 | 0.000 *** |

pair_trawl | 3.189 | 0.245 | 13.029 | <2e−16 *** |

stow_net | 2.509 | 0.245 | 10.249 | 0.000 *** |

pair_trawl:move23 | −2.023 | 0.395 | −5.124 | 0.000 *** |

stow_net:move23 | −2.601 | 0.395 | −6.59 | 0.000 *** |

pair_trawl:move24 | −4.065 | 0.307 | −13.248 | <2e−16 *** |

stow_net:move24 | −3.042 | 0.307 | −9.912 | 0.000 *** |

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**Figure 1.**Small yellow croaker catch by fishing type (

**a**) and number of vessels (

**b**) from 1992 to 2018.

**Figure 3.**Fishery ground ellipses computed using the catch per unit effort distribution of small yellow croakers in the three fisheries under different periods (

**a**) and the centers of fishing grounds in different fishing years (

**b**) [49].

**Figure 4.**Prior distributions (dashed line) and posterior distributions (solid line) of K and r assessed using the Bayesian state-space model.

**Figure 5.**Standardized catch per unit effort (CPUE) and the 2.5th (lower dotted line), 50th (median; red line), and 97.5th (upper dotted line) percentiles from the posterior distribution of CPUE based on the Bayesian state-space model using the Fox function as a non-informative prior distribution (inverse-gamma distribution) of the K assumption.

**Figure 6.**Change in the annual stock biomass trajectories with 95% confidence intervals with biomass at sustainable yield (B

_{MSY}) (

**a**) and catch in comparison with the maximum sustainable yield (

**b**) of small yellow croakers based on the Bayesian state-space model.

**Figure 7.**Forecasting changes in small yellow croaker biomass under total allowable catch scenarios based on the Bayesian state-space model with a historical line (yellow line).

**Table 1.**Summary of prior distributions used for the sensitivity analysis with the Bayesian state-space model.

Parameter | Informative Prior Distribution | Non-Informative Prior Distribution | |
---|---|---|---|

Uniform | Inverse-Gamma | ||

r | Lognormal (−1.1, 0.51^{2}) | Lognormal (−0.69, 0.51^{2}) | Lognormal (−0.69, 0.51^{2}) |

K | Inverse-lognormal (12.38, 0.75^{2}) | Uniform (10,000–100,000,000) | Inverse-gamma (0.01, 0.01) |

q | Inverse-gamma (1,1) | Inverse-gamma (1,1) | Inverse-gamma (1,1) |

${\sigma}^{2}$ | Inverse-gamma (3.79, 0.01) | Inverse-gamma (3.79, 0.01) | Inverse-gamma (3.79, 0.01) |

${\tau}^{2}$ | Inverse-gamma (1.71, 0.01) | Inverse-gamma (1.71, 0.01) | Inverse-gamma (1.71, 0.01) |

Parameter | Schaefer | Fox | ||||
---|---|---|---|---|---|---|

Informative K | Non-Informative K | Informative K | Non-Informative K | |||

Lognormal K | Uniform | Inverse-Gamma | Log-Normal K | Uniform | Inverse-Gamma | |

r | 0.4469 | 0.5426 | 0.5703 | 0.3273 | 0.3854 | 0.3738 |

K (ton) | 214,100 | 198,700 | 187,600 | 169,700 | 148,500 | 154,900 |

q | 2.03E-04 | 2.31E-04 | 2.46E-04 | 2.35E-04 | 2.72E-04 | 2.63E-04 |

MSY (maximum sustainable yield) | 23,920 | 26,954 | 26,747 | 20,433 | 21,054 | 21,301 |

B_{2018}/B_{MSY} | 0.85 | 0.82 | 0.82 | 1.24 | 1.22 | 1.21 |

${\sigma}^{2}$ | 1.16E-04 | 1.13E-04 | 1.10E-04 | 1.33E-04 | 1.46E-04 | 1.43E-04 |

${\tau}^{2}$ | 0.03117 | 0.03382 | 0.03559 | 0.01848 | 0.01402 | 0.01473 |

R^{2} | 0.96 | 0.96 | 0.95 | 0.99 | 0.99 | 0.99 |

DIC (deviance information criterion) | 149.599 | 150.050 | 150.953 | 142.938 | 139.631 | 139.226 |

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**MDPI and ACS Style**

Choi, M.-J.; Kim, D.-H.
Assessment and Management of Small Yellow Croaker (*Larimichthys polyactis*) Stocks in South Korea. *Sustainability* **2020**, *12*, 8257.
https://doi.org/10.3390/su12198257

**AMA Style**

Choi M-J, Kim D-H.
Assessment and Management of Small Yellow Croaker (*Larimichthys polyactis*) Stocks in South Korea. *Sustainability*. 2020; 12(19):8257.
https://doi.org/10.3390/su12198257

**Chicago/Turabian Style**

Choi, Min-Je, and Do-Hoon Kim.
2020. "Assessment and Management of Small Yellow Croaker (*Larimichthys polyactis*) Stocks in South Korea" *Sustainability* 12, no. 19: 8257.
https://doi.org/10.3390/su12198257