Arrowtooth Flounder (Atheresthes stomias) Stock Assessment for the West Coast of British Columbia in 2021

class: center, middle, inverse, title-slide

.title[
# Arrowtooth Flounder (<em>Atheresthes stomias</em>) Stock Assessment for the West Coast of British Columbia in 2021
]
.subtitle[
## Assessment model
]
.author[
### C. Grandin, S. Anderson, P. English
]
.institute[
### DFO
]
.date[
### Slides compiled on 2022-10-19
]

---

exclude: true

---
class: center, bg_arf
### Outline

.left[

- Introduction (biology and differences from last assessment)
- Management history, areas and spatial catch
- Data
  - Catch, Length, Age
  - Indices of Abundance
  - Growth parameters (fit outside assessment model)
  - Proportion female
- Bridge models
- Assessment model fits/estimates
  - Index fits, Age fits/residuals, Selectivity
  - Posterior distributions of MSY-based reference points
  - MCMC diagnostics
- Retrospective models
- Sensitivity models
- Projections and decision tables
- Summary
]
<div class="footer" id="a">
  <a href="https://www.seafoodwatch.org/recommendation/flounder/arrowtooth-flounder-525">Photo Source</a>
</div>

---
class: center, bg_arf_face_close
### Introduction

.left[
**Arrowtooth Flounder**
- are a flatfish that occurs in the offshore waters of British Columbia;
- mostly feed on Capelin, Euphausiids, Walleye Pollock, Pandalid shrimp, Herring, and other forage fish;
- are prey for mostly Pacific Cod, Pacific Halibut, and Steller sea lions; for juveniles, adult Arrowtooth Flounder and Walleye Pollock;
- are primarily caught by bottom trawl fishery, and sometimes by hook and line in the Halibut fishery;
- must be frozen shortly after catching due to proteolysis of the flesh;
- seasonal vertical migration to deeper water in winter, shallower in summer; and
- spawn and hatch in deeper water (>350m), in winter.

**The 2015 assessment model**
- included data from 1996-2014 and
- was done with a model which was female only and had a single commercial trawl fleet.
- Link to the .link-style1[[Research document](https://www.dfo-mpo.gc.ca/csas-sccs/Publications/ResDocs-DocRech/2017/2017_025-eng.html)]

**The 2021 assessment model**
- includes data from 1996-2021;
- includes 3 synoptic surveys (QCS, HS, and WCVI) and
- is split by sex, and has two commercial trawl fleets (Freezer trawlers and Shoreside).
]
<div class="footer" id="a">
  <a href="https://www.flickr.com/photos/77659781@N00/6150221707">Photo Source</a>
</div>

---
class: center
### Management

.left[
**Arrowtooth Flounder**
- are managed as a coastwide stock;
- had no limits on catch prior to 2006;
- had a TAC of 15,000 t in place from 2006-2017;
- had the TAC increased to 17,500 t in 2017 and
- had the TAC decreased to 14,000 t in 2019.

On Jan. 30, 2020, late changes to the Integrated Fisheries Management Plan (IFMP) to address declining abundance in the synoptic surveys were recommended. These changes included:
- reducing 2020/2021 TAC from 14,000 t to 5,000 t;
- reducing 2019/2020 carryover allowance from 30% to 10%;
- reducing the amount of temporary quota a license can hold from 16% to 8% of TAC and
- implementing new spatial closures from Nov. 1 to Mar. 31 to limit harvesting of spawning aggregations.

.link-style1[[IFMP for Groundfish](https://www.pac.dfo-mpo.gc.ca/fm-gp/mplans/ground-fond-ifmp-pgip-sm-eng.html)]
]

---
class: center
### Management Areas and catch
<img src="knitr-figs-docx/management-areas-1.png" width="900" style="display: block; margin: auto;" />

---
class: center
### Catch data

.left[
**Catch for Arrowtooth Flounder**
- had no discard reporting prior to 1996, when observers were introduced. Entire tows were often discarded without report;
- continued to be discarded at sea in great numbers until the arrival of freezer trawlers in the mid 2000's, which could freeze their catch at sea and avoid proteolysis;
- had large declines recently (2020-2021) which was due to TAC reductions
- was dominated by Freezer trawlers in the last decade.

**Notes on catch**
- The commercial fishing year for Arrowtooth Flounder starts on Feb 21 and ends on Feb 20. All yearly catch data in this assessment were aggregated in this way.

- Historical catch reconstruction was not attempted due to the unreported discards at sea prior to 1996.

- The large spike in 2005 catch was from a test fishery that took place in area 5D. There was an immediate drop the next year due to lack of profitability of the fishery, likely due to proteolysis and lack of freezers at sea.
]

---
class: center
### Catch by area
<img src="knitr-figs-docx/catch-by-area-1.png" width="900" style="display: block; margin: auto;" />

---
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### Catch by fleet

---
class: center
### Length data

---
class: center, bg_arf_pencil
### Age data
.left[
Age data were
- recorded using break-and-bake method where a whole tray of otoliths are baked and then individually broken and rings counted;

- chosen randomly across many vessels for the commercial trawl fishery;

- included for both commercial fleets and three synoptic surveys;

- input into the model as weighted proportions-at-age using the methods of Holt et. al (2016) and the 2015 Arrowtooth assessment. This method is coded into the `weight_comps()` function located in the .link-style1[[gfplot R package](https://github.com/pbs-assess/gfplot)].
]
<div class="footer" id="a">
  <a href="https://stock.adobe.com/images/arrowtooth-flounder-atheresthes-stomas-a-flatfish-from-the-north-pacific-in-top-view/317577516?as_campaign=ftmigration2&as_channel=dpcft&as_campclass=brand&as_source=ft_web&as_camptype=acquisition&as_audience=users&as_content=closure_asset-detail-page">Photo Source</a>
</div>

---
class: center
### Age data

---
class: center, bg_surveys
### Abundance Indices

.left[
Five fishery independent indices of abundance were fit in the base model:

- Queen Charlotte Sound Synoptic Survey: odd years, 2003&ndash;2021 and 2004

- Hecate Strait Multispecies Assemblage Survey: 1996, 1998, 2000,2002, 2003

- Hecate Strait Synoptic Survey: odd years, 2005&ndash;2021

- West Coast Vancouver Island Synoptic Survey: even years, 2004&ndash;2018, and 2021

- Discard CPUE Index: all years, 1996&ndash;2021

All are in thousands of tonnes except the Discard CPUE Index which is in kg/hr.
]
<div class="footer" id="a">
  <a href="https://www.researchgate.net/figure/Locations-of-the-current-groundfish-trawl-surveys-on-the-coast-of-British-Columbia_fig1_237497699">Photo Source</a>
</div>

---
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### Length/Weight fits by sex

---
class: center
### Length/Age fits

---
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### Age and length-at maturity ogives

---
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### Growth Parameters fit externally

<div id="tab:growth-params-table"><table><caption></caption><thead><tr class="header"><th style="text-align: left;">Parameter</th><th style="text-align: right;">Female</th><th style="text-align: right;">Male</th></tr></thead><tbody><tr class="odd"><td style="text-align: left;">Asymptotic length (<spanclass="math inline"><em>l</em><sub><em>i</em><em>n</em><em>f</em></sub></span>)</td><td style="text-align: right;">61.770</td><td style="text-align: right;">47.159</td></tr><tr class="even"><td style="text-align: left;">Brody growth coefficient (<spanclass="math inline"><em>k</em></span>)</td><td style="text-align: right;">0.182</td><td style="text-align: right;">0.274</td></tr><tr class="odd"><td style="text-align: left;">Theoretical age at zero length (<spanclass="math inline"><em>t</em><sub>0</sub></span>)</td><td style="text-align: right;">-0.479</td><td style="text-align: right;">-0.258</td></tr><tr class="even"><td style="text-align: left;">Scalar in length-weight allometry (<spanclass="math inline"><em>α</em></span>)</td><td style="text-align: right;">0.0000076</td><td style="text-align: right;">0.0000095</td></tr><tr class="odd"><td style="text-align: left;">Power parameter in length-weight allometry(<span class="math inline"><em>β</em></span>)</td><td style="text-align: right;">3.052</td><td style="text-align: right;">2.974</td></tr><tr class="even"><td style="text-align: left;">Age at 50% maturity (<spanclass="math inline"><em>ȧ</em></span>)</td><td style="text-align: right;">5.566</td><td style="text-align: right;">4.103</td></tr><tr class="odd"><td style="text-align: left;">SD at 50% maturity (<spanclass="math inline"><em>γ̇</em></span>)</td><td style="text-align: right;">0.911</td><td style="text-align: right;">1.247</td></tr></tbody></table></div>

---
class: center
### Proportion female

<table><tr valign="top"><td><table class="table table table table" style="font-size: 14px; margin-left: auto; margin-right: auto; margin-left: auto; margin-right: auto; font-size: 14px; margin-left: auto; margin-right: auto; margin-left: auto; margin-right: auto;">
<caption style="font-size: initial !important;"></caption>
 <thead>
  <tr>
   <th style="text-align:left;font-weight: bold;"> Year </th>
   <th style="text-align:left;font-weight: bold;"> Commercial trawl </th>
   <th style="text-align:left;font-weight: bold;"> QCS </th>
   <th style="text-align:left;font-weight: bold;"> HS </th>
   <th style="text-align:left;font-weight: bold;"> WCVI </th>
   <th style="text-align:left;font-weight: bold;"> WCHG </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> 1996 </td>
   <td style="text-align:left;"> 0.85 </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 1997 </td>
   <td style="text-align:left;"> 0.85 </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 1998 </td>
   <td style="text-align:left;"> 0.80 </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 1999 </td>
   <td style="text-align:left;"> 0.79 </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2000 </td>
   <td style="text-align:left;"> 0.78 </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2001 </td>
   <td style="text-align:left;"> 0.89 </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2002 </td>
   <td style="text-align:left;"> 0.88 </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2003 </td>
   <td style="text-align:left;"> 0.78 </td>
   <td style="text-align:left;"> 0.84 </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2004 </td>
   <td style="text-align:left;"> 0.89 </td>
   <td style="text-align:left;"> 0.88 </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> 0.85 </td>
   <td style="text-align:left;"> — </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2005 </td>
   <td style="text-align:left;"> 0.85 </td>
   <td style="text-align:left;"> 0.90 </td>
   <td style="text-align:left;"> 0.82 </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2006 </td>
   <td style="text-align:left;"> 0.86 </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> 0.85 </td>
   <td style="text-align:left;"> 0.76 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;"> 2007 </td>
   <td style="text-align:left;font-weight: bold;"> 0.84 </td>
   <td style="text-align:left;font-weight: bold;"> 0.76 </td>
   <td style="text-align:left;font-weight: bold;"> 0.78 </td>
   <td style="text-align:left;font-weight: bold;"> — </td>
   <td style="text-align:left;font-weight: bold;"> 0.81 </td>
  </tr>
</tbody>
</table></td><td><table class="table table table table" style="font-size: 14px; margin-left: auto; margin-right: auto; margin-left: auto; margin-right: auto; font-size: 14px; margin-left: auto; margin-right: auto; margin-left: auto; margin-right: auto;">
<caption style="font-size: initial !important;"></caption>
 <thead>
  <tr>
   <th style="text-align:left;font-weight: bold;"> Year </th>
   <th style="text-align:left;font-weight: bold;"> Commercial trawl </th>
   <th style="text-align:left;font-weight: bold;"> QCS </th>
   <th style="text-align:left;font-weight: bold;"> HS </th>
   <th style="text-align:left;font-weight: bold;"> WCVI </th>
   <th style="text-align:left;font-weight: bold;"> WCHG </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> 2008 </td>
   <td style="text-align:left;"> 0.92 </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> 0.85 </td>
   <td style="text-align:left;"> 0.86 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2009 </td>
   <td style="text-align:left;"> 0.68 </td>
   <td style="text-align:left;"> 0.80 </td>
   <td style="text-align:left;"> 0.75 </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2010 </td>
   <td style="text-align:left;"> 0.73 </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> 0.82 </td>
   <td style="text-align:left;"> 0.83 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2011 </td>
   <td style="text-align:left;"> 0.74 </td>
   <td style="text-align:left;"> 0.75 </td>
   <td style="text-align:left;"> 0.79 </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2012 </td>
   <td style="text-align:left;"> 0.83 </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> 0.75 </td>
   <td style="text-align:left;"> 0.84 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2013 </td>
   <td style="text-align:left;"> 0.77 </td>
   <td style="text-align:left;"> 0.72 </td>
   <td style="text-align:left;"> 0.73 </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2014 </td>
   <td style="text-align:left;"> 0.78 </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> 0.77 </td>
   <td style="text-align:left;"> 0.66 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2015 </td>
   <td style="text-align:left;"> 0.76 </td>
   <td style="text-align:left;"> 0.74 </td>
   <td style="text-align:left;"> 0.74 </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2016 </td>
   <td style="text-align:left;"> 0.77 </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> 0.72 </td>
   <td style="text-align:left;"> 0.82 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2017 </td>
   <td style="text-align:left;"> 0.76 </td>
   <td style="text-align:left;"> 0.75 </td>
   <td style="text-align:left;"> 0.77 </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2018 </td>
   <td style="text-align:left;"> 0.77 </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> 0.77 </td>
   <td style="text-align:left;"> 0.80 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2019 </td>
   <td style="text-align:left;"> 0.78 </td>
   <td style="text-align:left;"> 0.77 </td>
   <td style="text-align:left;"> 0.78 </td>
   <td style="text-align:left;"> — </td>
   <td style="text-align:left;"> — </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;"> Mean </td>
   <td style="text-align:left;font-weight: bold;"> 0.81 </td>
   <td style="text-align:left;font-weight: bold;"> 0.79 </td>
   <td style="text-align:left;font-weight: bold;"> 0.77 </td>
   <td style="text-align:left;font-weight: bold;"> 0.79 </td>
   <td style="text-align:left;font-weight: bold;"> 0.81 </td>
  </tr>
</tbody>
</table></td><tr></table>
.left[
The overall mean of the survey and the commercial fishery means is <SPAN STYLE="font-size:18.0pt">0.79</SPAN>

This was input into the ISCAM base model.
]

---
class: center, middle, inverse
# Bridge Models

---
class: center
### Bridge models - group 1

.left[
- Bridge models were run to move from the model used in the 2015 assessment to this year's assessment.
- Each of the 10 models has one has only one change to the model from the previous one.
]
<img src="knitr-figs-docx/bridge-biomass-group1-1.png" width="70%" style="display: block; margin: auto;" />

---
class: center
### Bridge models - Pairs plot resulting from adding data to 2021

---
class: center
### Bridge models - group 2

---
class: center
### Bridge models - Index fits for group 2 models

---
class: center
### Bridge models - Selectivity estimates for split-sex model
<img src="knitr-figs-docx/bridge-group2-sel-1.png" width="60%" style="display: block; margin: auto;" />

.left[
- The selectivity age-at-50% estimates `\((\hat{a})\)` for females and males in the West Coast Haida Gwaii Synoptic Survey for this model were (median, CI [credible interval]) 908,360 (46&ndash;21,893,582,500) and 94 (39&ndash;1,247) respectively.
]

---
class: center
### Bridge models - group 3

---
class: center
### Bridge models - Pairs plot resulting from removing WCHG

<img src="knitr-figs-docx/fig-bridge-pairs-remove-wchg-1.png" width="70%" style="display: block; margin: auto;" />
.left[
- This model has excessive correlation between parameters.
- M estimate of 0.19 (0.19&ndash;0.20) for males is too low for this stock compared to surrounding areas, and should be higher than the female estimate, 0.17 (0.16&ndash;0.18).
]

---
class: center
### Bridge models - Pairs plot resulting from fixing M

<img src="knitr-figs-docx/fig-bridge-pairs-fix-m-1.png" width="70%" style="display: block; margin: auto;" />
.left[
- Fixed M to 0.20 for females and 0.35 for males as in the GOA and Bering Sea/Aleutian Islands assessment.
- A higher male M is supported by a lack of older males in the survey and trawl data
]

---
class: center
### Bridge models - All models

---
class: center, bg_arf_pencil_flip
### Bridge models - Summary

.left[
The base model is the last bridge model and includes all changes made across the set of bridge models which include:

- switch to .link-style1[[gfdata](https://github.com/pbs-assess/gfdata)]/.link-style1[[gfplot](https://github.com/pbs-assess/gfplot)] methods for data extraction;
- updated age, catch, and index data to include 2015&ndash;2021;
- the Dirichlet-Multinomial age weighting parameterization;
- two-fleets for commercial trawl fishery (Freezer trawlers and Shoreside);
- addition of the Discard CPUE index;
- split-sex model;
- fishing year runs from Feb. 21 - Feb. 20 (instead of Jan. 1 - Dec. 31);
- removal of all data from West Coast Haida Gwaii Synoptic Survey and
- fixed natural mortality for both sexes (0.2 for females and 0.35 for males)
]
<div class="footer" id="a">
  <a href="https://stock.adobe.com/images/arrowtooth-flounder-atheresthes-stomas-a-flatfish-from-the-north-pacific-in-top-view/317577516?as_campaign=ftmigration2&as_channel=dpcft&as_campclass=brand&as_source=ft_web&as_camptype=acquisition&as_audience=users&as_content=closure_asset-detail-page">Photo Source</a>
</div>

---
class: center, middle, inverse
# Base model

---
class: center
### Base model - Abundance index fits

---
class: center
### Base model - Abundance index residuals

---
class: center
### Base model - Age fits/residuals for Freezer trawlers
.left-fig[
<img src="knitr-figs-docx/age-fits-base-ft-1.png" width="100%" style="display: block; margin: auto;" />
]
.right-fig[
<img src="knitr-figs-docx/age-resids-base-ft-1.png" width="100%" style="display: block; margin: auto;" />
]

---
class: center
### Base model - Age fits for Shoreside
.left-fig[
<img src="knitr-figs-docx/age-fits-base-ss-1-1.png" width="100%" style="display: block; margin: auto;" />
]
.right-fig[
<img src="knitr-figs-docx/age-fits-base-ss-2-1.png" width="100%" style="display: block; margin: auto;" />
]

---
class: center
### Base model - Age residuals for Shoreside

---
class: center
### Base model - Age fits/residuals for QCS Synoptic survey
.left-fig[
<img src="knitr-figs-docx/age-fits-base-qcs-1.png" width="100%" style="display: block; margin: auto;" />
]
.right-fig[
<img src="knitr-figs-docx/age-resids-base-qcs-1.png" width="100%" style="display: block; margin: auto;" />
]

---
class: center
### Base model - Age fits/residuals for HS Synoptic survey
.left-fig[
<img src="knitr-figs-docx/age-fits-base-hss-1.png" width="100%" style="display: block; margin: auto;" />
]
.right-fig[
<img src="knitr-figs-docx/age-resids-base-hss-1.png" width="100%" style="display: block; margin: auto;" />
]

---
class: center
### Base model - Age fits/residuals for WCVI Synoptic survey
.left-fig[
<img src="knitr-figs-docx/age-fits-base-wcvi-1.png" width="100%" style="display: block; margin: auto;" />
]
.right-fig[
<img src="knitr-figs-docx/age-resids-base-wcvi-1.png" width="100%" style="display: block; margin: auto;" />
]

---
class: center
### Base model - Dirichlet Multinomial parameters and effective sample sizes, 1996&ndash;2007

---
class: center
### Base model - Dirichlet Multinomial parameters and effective sample sizes, 2008&ndash;2021

---
class: center
### Base model - Selectivity estimates
.left[
Selectivities were estimated for the gears with age compositions; the two trawl fleets and the three synoptic surveys (not including WCHG).
- Maturities are shown on the plots (dashes lines) to show why the vulnerable biomass was estimated so small, the selectivities are almost all estimated to the right of the maturities, especially the males.
- Single blue lines represent fixed selectivities; both sexes were fixed the the same value.

<img src="knitr-figs-docx/selex-base-1.png" width="60%" style="display: block; margin: auto;" />
]

---
class: center
### Base model - Reference point estimates
.left[
- The `\(U_{MSY_2}\)` posteriors (exploitation rate) for the Shoreside fleet are all at or near 1, meaning the fishing mortality is unrealistically large.
- This implies that no amount of fishing would impact the stock, and is why the MSY-based reference points are so liberal.

<img src="knitr-figs-docx/ref-points-base-1.png" width="60%" style="display: block; margin: auto;" />
]

---
class: center, middle, inverse
# Base Model &mdash; MCMC diagnostics

---
class: center
### Base model - Priors and Posteriors

<img src="knitr-figs-docx/mcmc-base-priors-posts-1.png" width="70%" style="display: block; margin: auto;" />
.left[
- Subscript on catchability  parameters, `\(q_k\)`:
- `\(k\)` = Gear: `\(1\)` = QCS Synoptic, `\(2\)` = HS Multi. Assemb., `\(3\)` = HS Synoptic, `\(4\)` = WCVI Synoptic, `\(5\)` = Discard CPUE
]

---
class: center
### Base model - Traceplots, leading parameters

<img src="knitr-figs-docx/mcmc-base-trace-1.png" width="70%" style="display: block; margin: auto;" />
.left[
- Subscript on catchability  parameters, `\(q_k\)`:
- `\(k\)` = Gear: `\(1\)` = QCS Synoptic, `\(2\)` = HS Multi. Assemb., `\(3\)` = HS Synoptic, `\(4\)` = WCVI Synoptic, `\(5\)` = Discard CPUE
]

---
class: center
### Base model - Traceplots, selectivity parameters
<img src="knitr-figs-docx/mcmc-base-trace-selex-1.png" width="65%" style="display: block; margin: auto;" />
.left[
- Subscripts on selectivity parameters, `\(\hat{a}_{g,s,t}\)` and `\(\hat{\gamma}_{g,s,t}\)`:
  - `\(g\)` = Gear: `\(1\)` = Freezer trawlers, `\(2\)` = Shoreside, `\(3\)` = QCS Synoptic, `\(5\)` = HS Synoptic, `\(6\)` = WCVI Synoptic
  - `\(s\)` = Sex: `\(f\)` = Female, `\(m\)` = Male
  - `\(t\)` = Time block (for TV selectivity, all are `\(1\)` here because base model has time-invariant selectivity)
]

---
class: center
### Base model - Autocorrelation, leading parameters

<img src="knitr-figs-docx/mcmc-base-autocor-1.png" width="70%" style="display: block; margin: auto;" />
.left[
- Subscript on catchability  parameters, `\(q_k\)`:
- `\(k\)` = Gear: `\(1\)` = QCS Synoptic, `\(2\)` = HS Multi. Assemb., `\(3\)` = HS Synoptic, `\(4\)` = WCVI Synoptic, `\(5\)` = Discard CPUE
]

---
class: center
### Base model - Autocorrelation, selectivity parameters

<img src="knitr-figs-docx/mcmc-base-autocor-selex-1.png" width="65%" style="display: block; margin: auto;" />
.left[
- Subscripts on selectivity parameters, `\(\hat{a}_{g,s,t}\)` and `\(\hat{\gamma}_{g,s,t}\)`:
  - `\(g\)` = Gear: `\(1\)` = Freezer trawlers, `\(2\)` = Shoreside, `\(3\)` = QCS Synoptic, `\(5\)` = HS Synoptic, `\(6\)` = WCVI Synoptic
  - `\(s\)` = Sex: `\(f\)` = Female, `\(m\)` = Male
  - `\(t\)` = Time block (for TV selectivity, all are `\(1\)` here because base model has time-invariant selectivity)
]

---
class: center
### Pairs plot - base model, leading parameters
<img src="knitr-figs-docx/fig-base-pairs-1.png" width="70%" style="display: block; margin: auto;" />
.left[
- Subscript on catchability  parameters, `\(q_k\)`:
- `\(k\)` = Gear: `\(1\)` = QCS Synoptic, `\(2\)` = HS Multi. Assemb., `\(3\)` = HS Synoptic, `\(4\)` = WCVI Synoptic, `\(5\)` = Discard CPUE
]

---
class: center
### Pairs plot - base model, selectivity parameters
<img src="knitr-figs-docx/fig-base-pairs-sel-1.png" width="65%" style="display: block; margin: auto;" />
.left[
- Subscripts on selectivity parameters, `\(\hat{a}_{g,s,t}\)` and `\(\hat{\gamma}_{g,s,t}\)`:
  - `\(g\)` = Gear: `\(1\)` = Freezer trawlers, `\(2\)` = Shoreside, `\(3\)` = QCS Synoptic, `\(5\)` = HS Synoptic, `\(6\)` = WCVI Synoptic
  - `\(s\)` = Sex: `\(f\)` = Female, `\(m\)` = Male
  - `\(t\)` = Time block (for TV selectivity, all are `\(1\)` here because base model has time-invariant selectivity)
]

---
class: center
### Comparison of Base model and single sex model (bridge model 2)

---
class: center, middle, inverse
# Retrospective models

---
class: center
### Retrospectives - Spawning biomass
<img src="knitr-figs-docx/fig-retro-biomass-1.png" width="85%" style="display: block; margin: auto;" />

---
class: center
### Retrospectives - Spawning biomass, closer view
<img src="knitr-figs-docx/fig-retro-biomass-closer-1.png" width="85%" style="display: block; margin: auto;" />

---
class: center
### Retrospectives - Relative spawning biomass
<img src="knitr-figs-docx/fig-retro-biomass-rel-1.png" width="85%" style="display: block; margin: auto;" />

---
class: center
### Retrospectives - Recruitment
<img src="knitr-figs-docx/fig-retro-recr-1.png" width="85%" style="display: block; margin: auto;" />

---
class: center
### Retrospectives - Recruitment, closer view
<img src="knitr-figs-docx/fig-retro-recr-closer-1.png" width="85%" style="display: block; margin: auto;" />

---
class: center
### Retrospectives - Fishing mortality by fleet
<img src="knitr-figs-docx/fig-retro-f-1.png" width="85%" style="display: block; margin: auto;" />

---
class: center
### Retrospectives - Index fits
<img src="knitr-figs-docx/fig-retro-index-fits-1.png" width="85%" style="display: block; margin: auto;" />

---
class: center
### Retrospectives - Trace plots for 2019 model
<img src="knitr-figs-docx/fig-base-trace-selex-1.png" width="85%" style="display: block; margin: auto;" />

---
class: center
### Retrospectives - Pairs plot for 2019 model
<img src="knitr-figs-docx/fig-base-pairs-retro-1.png" width="85%" style="display: block; margin: auto;" />

---
class: center
### Comparison of 2015 model and retrospective for 2015

---
class: center, middle, inverse
# Sensitivity models

---
class: center
### Sensitivity group 1 - Spawning biomass
<img src="knitr-figs-docx/fig-sens1-1.png" width="70%" style="display: block; margin: auto;" />
.left[
- Two `\(B_0\)` values were left off the plot for clarity.
- They are estimated as 445 (236–602) thousand t and 370 (200–581) thousand t for the "Decrease `\(\sigma\)` to 0.135" and "Increase `\(\tau\)` to 1.0" respectively.

]

---
class: center
### Sensitivity group 1 - Relative spawning biomass
<img src="knitr-figs-docx/fig-sens1-rel-1.png" width="85%" style="display: block; margin: auto;" />

---
class: center
### Reducing steepness prior mean from 0.8 to 0.72 - Priors vs. Posteriors
<img src="knitr-figs-docx/sens-steepness-prior-1.png" width="65%" style="display: block; margin: auto;" />
.left[
- Subscript on catchability  parameters, `\(q_k\)`:
- `\(k\)` = Gear: `\(1\)` = QCS Synoptic, `\(2\)` = HS Multi. Assemb., `\(3\)` = HS Synoptic, `\(4\)` = WCVI Synoptic, `\(5\)` = Discard CPUE
]

---
class: center
### Sensitivity group 3 - Spawning biomass
<img src="knitr-figs-docx/fig-sens3-1.png" width="85%" style="display: block; margin: auto;" />

---
class: center
### Sensitivity group 3 - Relative spawning biomass
<img src="knitr-figs-docx/fig-sens3-rel-1.png" width="85%" style="display: block; margin: auto;" />

---
class: center
### Sensitivity group 3 - Catchability estimates
<img src="knitr-figs-docx/fig-sens3-q-1.png" width="85%" style="display: block; margin: auto;" />

---
class: center
### Sensitivity group 4 - Spawning biomass
<img src="knitr-figs-docx/fig-sens4-1.png" width="85%" style="display: block; margin: auto;" />

---
class: center
### Sensitivity group 4 - Relative spawning biomass
<img src="knitr-figs-docx/fig-sens4-rel-1.png" width="85%" style="display: block; margin: auto;" />

---
class: center
### Sensitivity group 4 - Vulnerable biomass
<img src="knitr-figs-docx/fig-sens4-vuln-1.png" width="70%" style="display: block; margin: auto;" />
.left[
- The two trawl fleets have their selectivity set equal so their vulnerable biomasses overlap
- The ratio of the sum of the two fleets’ vulnerable biomasses to the spawning biomass in 2021 is 0.23
- For the base model, this ratio is 0.15
]

---
class: center
### Sensitivity group 4 - Index fits
<img src="knitr-figs-docx/fig-sens4-index-fits-1.png" width="85%" style="display: block; margin: auto;" />

---
class: center
### Sensitivity To QCS time-varying selectivity - Selectivity estimates
<img src="knitr-figs-docx/fig-sens4-qcs-tv-selex-1.png" width="85%" style="display: block; margin: auto;" />

---
class: center
### Sensitivity To QCS time-varying selectivity - Trace plots
<img src="knitr-figs-docx/fig-sens4-qcs-trace-1.png" width="85%" style="display: block; margin: auto;" />

---
class: center
### Sensitivity for Geostatistical-based index - Spawning biomass
<img src="knitr-figs-docx/fig-sens5-1.png" width="85%" style="display: block; margin: auto;" />

---
class: center
### Sensitivity for Geostatistical-based index - Relative spawning biomass
<img src="knitr-figs-docx/fig-sens5-rel-1.png" width="85%" style="display: block; margin: auto;" />

---
class: center
### Sensitivity  for Geostatistical-based index - Index fits
<img src="knitr-figs-docx/fig-sens5-index-fits-1.png" width="85%" style="display: block; margin: auto;" />

---
class: center, middle, inverse
### Projections, decision table, and summary

---
class: center
### Decision table and figure of outcomes
.left-fig[
<table class="table table table table" style="font-size: 10px; margin-left: auto; margin-right: auto; margin-left: auto; margin-right: auto; font-size: 10px; margin-left: auto; margin-right: auto; margin-left: auto; margin-right: auto;">
<caption style="font-size: initial !important;"></caption>
 <thead>
  <tr>
   <th style="text-align:right;"> Catch (thousand t) </th>
   <th style="text-align:right;"> \(P(B_{2023} &lt; 0.2B_{0})\) </th>
   <th style="text-align:right;"> \(P(B_{2023} &lt; 0.4B_{0})\) </th>
   <th style="text-align:right;"> \(P(B_{2023} &lt; B_{2022})\) </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 0.000 </td>
   <td style="text-align:right;"> 0.491 </td>
   <td style="text-align:right;"> 0.007 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 0.000 </td>
   <td style="text-align:right;"> 0.583 </td>
   <td style="text-align:right;"> 0.189 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 4 </td>
   <td style="text-align:right;"> 0.000 </td>
   <td style="text-align:right;"> 0.676 </td>
   <td style="text-align:right;"> 0.627 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 6 </td>
   <td style="text-align:right;"> 0.000 </td>
   <td style="text-align:right;"> 0.749 </td>
   <td style="text-align:right;"> 0.863 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 8 </td>
   <td style="text-align:right;"> 0.000 </td>
   <td style="text-align:right;"> 0.810 </td>
   <td style="text-align:right;"> 0.952 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 10 </td>
   <td style="text-align:right;"> 0.003 </td>
   <td style="text-align:right;"> 0.870 </td>
   <td style="text-align:right;"> 0.978 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 11 </td>
   <td style="text-align:right;"> 0.008 </td>
   <td style="text-align:right;"> 0.892 </td>
   <td style="text-align:right;"> 0.985 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 12 </td>
   <td style="text-align:right;"> 0.009 </td>
   <td style="text-align:right;"> 0.914 </td>
   <td style="text-align:right;"> 0.991 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 13 </td>
   <td style="text-align:right;"> 0.014 </td>
   <td style="text-align:right;"> 0.932 </td>
   <td style="text-align:right;"> 0.992 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 14 </td>
   <td style="text-align:right;"> 0.021 </td>
   <td style="text-align:right;"> 0.938 </td>
   <td style="text-align:right;"> 0.993 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 15 </td>
   <td style="text-align:right;"> 0.030 </td>
   <td style="text-align:right;"> 0.951 </td>
   <td style="text-align:right;"> 0.995 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 16 </td>
   <td style="text-align:right;"> 0.039 </td>
   <td style="text-align:right;"> 0.959 </td>
   <td style="text-align:right;"> 0.996 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 17 </td>
   <td style="text-align:right;"> 0.056 </td>
   <td style="text-align:right;"> 0.966 </td>
   <td style="text-align:right;"> 0.998 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 18 </td>
   <td style="text-align:right;"> 0.067 </td>
   <td style="text-align:right;"> 0.971 </td>
   <td style="text-align:right;"> 0.998 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 19 </td>
   <td style="text-align:right;"> 0.084 </td>
   <td style="text-align:right;"> 0.977 </td>
   <td style="text-align:right;"> 0.998 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 20 </td>
   <td style="text-align:right;"> 0.108 </td>
   <td style="text-align:right;"> 0.978 </td>
   <td style="text-align:right;"> 0.998 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 22 </td>
   <td style="text-align:right;"> 0.156 </td>
   <td style="text-align:right;"> 0.987 </td>
   <td style="text-align:right;"> 0.998 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 24 </td>
   <td style="text-align:right;"> 0.211 </td>
   <td style="text-align:right;"> 0.988 </td>
   <td style="text-align:right;"> 0.999 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 26 </td>
   <td style="text-align:right;"> 0.273 </td>
   <td style="text-align:right;"> 0.990 </td>
   <td style="text-align:right;"> 0.999 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 28 </td>
   <td style="text-align:right;"> 0.334 </td>
   <td style="text-align:right;"> 0.990 </td>
   <td style="text-align:right;"> 0.999 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 30 </td>
   <td style="text-align:right;"> 0.418 </td>
   <td style="text-align:right;"> 0.994 </td>
   <td style="text-align:right;"> 1.000 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 50 </td>
   <td style="text-align:right;"> 0.953 </td>
   <td style="text-align:right;"> 1.000 </td>
   <td style="text-align:right;"> 1.000 </td>
  </tr>
</tbody>
</table>
]
.right-fig[
<img src="knitr-figs-docx/fig-proj-tac-1.png" width="100%" style="display: block; margin: auto;" />
.left[
- Thick lines are the 50% CI
- Thin lines are the 95% CI
- Points are medians
]
]

---
class: center, bg_arf
### Summary
.left[
- The inclusion of the 2015&ndash;2021 data are what changes the model the most
- The abundance has been declining sharply in the survey indices since 2018
- The discard CPUE shows a decline since 2013
- TAC was reduced to 5,000 t in 2020
- The spawning biomass has flattened out since 2020
- Recruitment is highly uncertain for 2020 and 2021
- The QCS survey index is difficult to fit, as it is not declining in the same way as other indices
- The QCS selectivity is estimated poorly in the retrospectives prior to 2019, and some sensitivities
- There is a lack of older males in the data which the model explains with a high M on males

**Thanks**

We thank members of the Arrowtooth Flounder Technical Working Group (Robyn Forrest, Rowan Haigh, Paul Starr, Diedre Finn, Rob Tadey, Bruce Turris, and Brian Mose) for their valuable advice and insights throughout this project. We thank members of the Sclerochronology Laboratory at the Pacific Biological Station for their processing of Arrowtooth Flounder otoliths.

We thank the reviewers for their careful reviews, which uncovered structural issues that would have otherwise been missed. This highlights the importance of independent peer review in the advisory process.
]
<div class="footer" id="a">
  <a href="https://www.seafoodwatch.org/recommendation/flounder/arrowtooth-flounder-525">Photo Source</a>
</div>