Modeling Discards in Stock Assessments: Red Grouper Epinephelus morio in the U.S. Gulf of Mexico
Abstract
:1. Introduction
2. Materials and Methods
2.1. Description of Discard Models and Simulations
2.1.1. Population and Fishery Dynamics
2.1.2. Retention-Function Approach
2.1.3. Separate-Fleet Approach
2.1.4. Simulation Scenarios
2.2. Case Study: Gulf Red Grouper
2.2.1. Base Model Configuration
2.2.2. Alternative Model Configurations
3. Results
3.1. Simulation Examples
3.2. Gulf Red Grouper Case Study
3.2.1. Comparison of Derived Quantities
3.2.2. Comparison of Benchmarks
3.2.3. Fleet-Specific Trends in Exploitation Rate
3.2.4. Exploitation Patterns
4. Discussion
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Parameter | Description | Value |
---|---|---|
General | ||
M | Natural mortality rate | 0.2 |
R | Expected recruitment in the absence of deviations | 1e6 |
Standard deviation of recruitment deviations (log space) | 0.5 | |
δ | Release mortality rate | 0.25 |
Slope parameter of catch selectivity | 4.0 | |
Location parameter of catch selectivity | 1.5 | |
Base-level fishing rate | 0.3 | |
Standard deviation of fishing rate deviations (log space) | 0.2 | |
Simulation 1 | ||
Slope parameter of retention function | 2.0 | |
Location parameter of retention function | 3.0 | |
p | Asymptotic retention | 1.0 |
Simulation 2 | ||
Slope parameter of retention function, years 1–10 | 2.0 | |
Location parameter of retention function, years 1–10 | 3.0 | |
Slope parameter of retention function, years 11–20 | 4.0 | |
Location parameter of retention function, years 11–20 | 5.0 | |
p | Asymptotic retention | 1.0 |
Simulation 3 | ||
Slope parameter of retention function | 2.0 | |
Location parameter of retention function | 3.0 | |
p | Asymptotic retention, increases linearly over years | (0.5, …, 1.0) |
Simulation 4 | ||
Slope parameter of retention function, years 1–10 | 2.0 | |
Location parameter of retention function, years 1–10 | 3.0 | |
Slope parameter of retention function, years 11–20 | 4.0 | |
Location parameter of retention function, years 11–20 | 5.0 | |
p | Asymptotic retention, varies randomly over years | p~U (0.5, 1.0) |
Main Change | Retention Model— 2 Blocks (Base) | Retention Model— Annual Blocks | Separate-Fleet Model |
---|---|---|---|
Model Evaluation | |||
Negative log likelihood (NLL) | 537.486 | 544.787 | 536.053 |
Catch NLL | 36.5 | 34.5 | 3.18 |
Survey NLL | −102.6 | −108 | −98.9 |
Discard NLL | −30.1 | −31.4 | - |
Length composition NLL | 287.3 | 300.3 | 292.2 |
Age composition NLL | 335.5 | 338.4 | 322.9 |
NLL maximum gradient | 0.000105 | 0.000225 | 0.009656 |
Number of estimated parameters | 178 | 250 | 298 |
Number of parameters with coefficient of variation (CV) > 1 (type of parameters) | 8 (Recruitment deviations) | 37 (Recruitment deviations, retention) | 35 (Fs, recruitment deviations, discard fleet selectivities) |
Key Parameter Estimates (CV) | |||
Recruitment variability () | 0.815 (0.114) | 0.811 (0.138) | 0.874 (0.140) |
Natural log of virgin recruitment [ln(R0)] | 9.925 (0.004) | 9.933 (0.004) | 9.779 (0.005) |
Commercial vertical line initial F (y−1) | 0.129 (0.187) | 0.130 (0.187) | 0.233 (0.448) |
Commercial longline initial F (y−1) | 0.09 (0.200) | 0.091 (0.201) | 0.201 (0.544) |
Commercial trap initial F (y−1) | 0.019 (0.219) | 0.02 (0.220) | 0.04 (1.163) |
Recreational initial F (y−1) | 0.245 (0.204) | 0.246 (0.205) | 0.239 (0.190) |
Red tide mortality in 2005 (y−1) | 0.339 (0.309) | 0.269 (0.401) | 0.398 (0.301) |
Red tide mortality in 2014 (y−1) | 0.257 (0.429) | 0.286 (0.396) | 0.117 (1.141) |
Criteria | Definition | Retention Model—2 Blocks (Base) | Retention Model—Annual Blocks | Separate-Fleet Model |
---|---|---|---|---|
Mortality Rate Criteria | ||||
FMSYproxy = Maximum Fishing Mortality Threshold (MFMT) | Equilibrium fishing mortality that achieves a spawning potential ratio (SPR) of 30% | 0.26 | 0.26 | 0.29 |
FCurrent | Average fishing mortality over last three years (2015–2017) | 0.20 | 0.21 | 0.24 |
FCurrent/MFMT | Current fishery status | 0.78 | 0.79 | 0.82 |
Overfishing in 2017? | No | No | No | |
Biomass Criteria | ||||
SSBMSYproxy | Equilibrium SSB when fishing at FMSYproxy | 748,241 | 754,383 | 646,482 |
Minimum Stock Size Threshold (MSST) | 0.5×SSBMSYproxy | 374,120 | 377,192 | 323,241 |
SSB0 | Virgin SSB | 2,494,130 | 2,513,280 | 2,153,750 |
SSB2017 | SSB in terminal year | 613,517 | 620,817 | 464,086 |
SSB2017/MSST | Current stock status | 1.64 | 1.65 | 1.44 |
Overfished in 2017? | No | No | No |
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Shertzer, K.W.; Williams, E.H.; Sagarese, S.R. Modeling Discards in Stock Assessments: Red Grouper Epinephelus morio in the U.S. Gulf of Mexico. Fishes 2022, 7, 7. https://doi.org/10.3390/fishes7010007
Shertzer KW, Williams EH, Sagarese SR. Modeling Discards in Stock Assessments: Red Grouper Epinephelus morio in the U.S. Gulf of Mexico. Fishes. 2022; 7(1):7. https://doi.org/10.3390/fishes7010007
Chicago/Turabian StyleShertzer, Kyle W., Erik H. Williams, and Skyler R. Sagarese. 2022. "Modeling Discards in Stock Assessments: Red Grouper Epinephelus morio in the U.S. Gulf of Mexico" Fishes 7, no. 1: 7. https://doi.org/10.3390/fishes7010007