class: center, middle, inverse, title-slide # Sablefish Operating Model Overview ## PSTAT ‘in person’ meeting ### M Sosa Kapur
kapurm@uw.edu
### 28/29 Apr 2020 --- layout: true .header[
@mkapur/sab-mse/] --- # Objectives + Provide overview of Operating Model design (beta, obviously) + Discuss assumptions, data inputs & treatment -- ## Outline + 30,000 foot view: model structure + Data Generation & OM Conditioning + Walk-through details from [document](LINK ME.PDF) + Discuss as we go (interrupt me 😄) ??? Don't forget that it is easy to add n selex curves, harder to change the array structure --- background-image: url("https://www.thoughtco.com/thmb/Bt4hhUDgr_LhLP5hEh6pP_2o2iM=/768x0/filters:no_upscale():max_bytes(150000):strip_icc()/closed-lift-door-1051317118-5c64607a46e0fb0001587ce5.jpg") background-size: cover <br><br><br> # .inverse[Ground Floor] --- # Ground Floor + OM is written in `R` + Conditioning/estimation happens in `TMB` + We are `not` shooting to replicate Stock Synthesis (etc.) exactly in structure nor estimated quantities --- # Spatial Structure + A little more complicated than expected (Figure 1) ![](img/Fig1_strata_panel.png) -- + Let's walk through how these came about --- # Spatial Structure <img src="img/Fig1_strata_mapsA.png" width="500" height="400" style="display: block; margin: auto;" /> ??? Also -- Space is confusing, so let's abstract these --- # Management Regions <img src="img/Fig1_strata_mapsA2.png" width="500" height="400" style="display: block; margin: auto;" /> --- ## Stock (demography) <img src="img/Fig1_strata_mapsB.png" width="500" height="400" style="display: block; margin: auto;" /> ??? --- ## Sub-Areas (what's modeled) <img src="img/Fig1_strata_mapsC.png" width="500" height="400" style="display: block; margin: auto;" /> --- ### Putting it all together (fleets + surveys) ![](./img/Fig1_strata_panel.png) ?? next up is what happens where -- but pause for any questions --- # What happens where ## Management Regions `\(m\)` .pull-left[ Alaska (.inverse[A]K), British Columbia (.inverse[B]C), Cal. Current (.inverse[C]C) + Contain fleets + Accrue catches + Set ABCs (future) ] .pull-right[ ![](img/Fig1_strata_mapsA2.png) ] --- # What happens where ## Stocks `\(k\)` .pull-left[ R1:R5, as in Kapur et al. (2020) + Share params for growth, maturity(?), density-dependence + SRR operates @ `\(k\)` and is partitioned ] .pull-right[ ![](img/Fig1_strata_mapsB.png) ] ??? stock is actually unit of interest --- # What happens where ## Sub-areas `\(i,j\)` .pull-left[ + A,B,C = AK-, BC-, CC-nested + Strata @ which populations are modeled (e.g. `\(N_a^i\)`) ] .pull-right[ ![](img/Fig1_strata_mapsC.png) ] ??? A table with all subscript & param definitions is provided near the end of the OM document. --- background-image: url("https://dynaimage.cdn.cnn.com/cnn/q_auto,h_600/https%3A%2F%2Fcdn.cnn.com%2Fcnnnext%2Fdam%2Fassets%2F191202162449-ingredients-to-longevity-3.jpg") background-size: cover <br><Br> # .inverse[Data Inputs] --- # Data Inputs .inverse[Catches & Comps] ![](img/Fig2_Fleets.png) -- + `Fixed Gear` for CC is Hook & Line + Pot + any others to combine/add/drop? ??? This is figure 2 Recall that some survey fleets were "collapsed" for VAST --- ## Data Inputs .inverse[Surveys] <img src="img/Fig2_OM_Indices.png" width="500" height="300" style="display: block; margin: auto;" /> Note that these are novel "fleets" not equivalent to survey comps fleets. --- ## Data Inputs .inverse[Demography] <img src="img/OMGrowthCurves.png" width="500" height="350" style="display: block; margin: auto;" /> `\(\sigma_G\)` now at individual strata --- background-image: url("https://www.thespruceeats.com/thmb/nsjMWi7TBf7AVMBFulYM3XQOYiQ=/2400x1350/smart/filters:no_upscale()/bowl-chili-98839917-56a8c4ab3df78cf772a0723d.jpg") background-size: cover <br><br><br> # .inverse[Data Generation] --- # Data Generation .inverse[What comes out of the OM?] Time series of... + Surveyed abundance, by fleet + Age & Length compositions, by fleet (where applicable) + Catch & discards + Numbers-at-age/length + Biomass + Parameters e.g. `\(F\)`, selectivity, `\(R_0\)` -- ...All of which can be used as .inverse[input data] or .inverse[parameter inits] in future EMs. --- background-image: url("http://bit.ly/cs631-donkey") background-size: cover <Br><Br><Br><Br><Br><Br> # .inverse[Take a break?] ??? conditioning & dynamics is next --- background-image: url("https://media.giphy.com/media/10uVasOeFs6U92/giphy.gif") background-size: cover <br><br><br> # .inverse[Model Conditioning] --- # Model Conditioning ## Approach + Template Model Builder w/ modular structure (see SAM) + Starter equations under "Likelihood Components", page 13 + Let's discuss general objectives, and get into details in tandem with dynamics --- # Model Conditioning ## Objectives + Fit the input data + Roughly reproduce trends from regional assessments + .inverse[others?] ??? In the dynamics section, when I walk thru equations I will include standout likelihood issues/estimation questions --- background-image: url("https://www.vaughn.edu/wp-content/uploads/2019/04/Math-Equations-on-Chalkboard-1024x407.jpg") background-size: cover <Br><Br><Br><Br><Br><Br> # .inverse[Operating Model Dynamics] ### .inverse[...and conditioning concerns] --- # OM Dynamics **Equation in Document** + Key assumptions -- + Conditioning concerns (if applicable) -- + .inverse[Discussion Points] --- # .small[Numbers at Age] .small[ `\(N_{y+1,\gamma,a}^i=\left\{\begin{matrix}0.5R_{y+1}^i & \text{if}\ a = 0 \newline \sum_{i\neq j}\left[\left(1-\textbf{X}_a^{i,j}\right)\left.\ {N_{y,\gamma,a-1}^ie}^{-Z_{y,\gamma,a-1}^i}\right.+\textbf{X}_a^{j,i}{N_{y,\gamma,a-1}^je}^{-Z_{y,\gamma,a-1}^i}\right] & \text{if}\ 1 \leq a <A\\\sum_{i\neq j}{\left[\left(1-\textbf{X}_a^{i,j}\right)(\left.{N_{y,\gamma,A-1}^ie}^{-Z_{y,\gamma,A-1}^i}\right.\left.+{N_{y,\gamma,A-1}^ie}^{-Z_{y,\gamma,A-1}^i}\right.)\right.\ } & \text{if}\ a = A \\\ldots+\left.\textbf{X}_a^{j,i}\left({N_{y,\gamma,A}^je}^{-Z_{y,\gamma,A}^j}+{N_{y,\gamma,A-1}^je}^{-Z_{y,\gamma,A-1}^j}\right)\right]\\\end{matrix}\right.\)` ] **Eq 1** + Yearly timestep + Monitored by sub-area `\(i\)` + Movement defined by `\(\textbf{X}^{i,j}_a\)` + .inverse[Plus group for age] --- # Growth I [general] `\(L_{y+1,\gamma,a}^i=L_{y,\gamma,a}^i+(L_{\infty,\gamma}^i-L_{y,\gamma,a}^i)\left(1-e^{-\kappa_\gamma^i}\right)\ if\ a\ <\ A\)` **Eq 2** + Growth indexed by stock `\(k\)` via Kapur et al. (2020) + Plus group via weighted average **Eq 3** + .inverse[Plus group for length: 50cm] --- # Growth II [after movement] `\(L_{y+1,\gamma,a}^i=\phi_{ij}\frac{N_{y+1,\gamma,a}^iL_{y,\gamma,a}^i+N_{y+1,\gamma,A}^jL_{y,\gamma,a}^j}{N_{y+1,\gamma,a}^i+N_{y+1,\gamma,a}^j}\)` **Eq 5** + Unlike SS, no growth "morphs" + Incoming fish influence `\(L^i_a\)` similar to plus-group ??? If fish moves to a new sub-area, it influences the mean length in that sub-area, then obtains growth patterns & corresponding movement probabilities from its sub-area `\(i\)` of residence Theoretically this could induce shrinkage, but hopefully most of the movement isn't north to south which would cause this to happen. Part of the rationale is that we would otherwise need to track individual growth histories and end up with an IBM like situation: if fish from A1 move to B2 then a bunch move to C2 etc. Instead, the new movement probs AND growth patterns are shared for everyone extant in sub-area i. --- # Length to Weight .small[ `\(\widetilde{\textbf{L}_{y,\gamma,a,l}^i}=\left\{\begin{matrix}\mathrm{\Phi}(\theta_1,\widetilde{L_{y,\gamma,a}^i},\sigma_{y,\gamma}^i)&if\ l\ =\ 1\\\mathrm{\Phi}(\theta_{l+1},\widetilde{L_{y,\gamma,a}^i},\sigma_{y,\gamma}^i)-\mathrm{\Phi}(\theta_l,\widetilde{L_{y,\gamma,a}^i},\sigma_{y,\gamma}^i)&if\ 1\ <l\ <\ A_l\\1-\mathrm{\Phi}(\theta_l,\widetilde{L_{y,\gamma,a}^i},\sigma_{y,\gamma}^i)&if\ l\ =\ \ A_l\\\end{matrix}\right.\)` ] `\(w_{\gamma,l}^i=\alpha_\gamma^i{\bar{L_l}}^{\beta_\gamma^i}\)` **Eqs 7, 9** + `\(\alpha, \beta\)` .inverse[vary by stock] + different `\(w^{f}_{a}\)` for catches --- # Reproduction I `\(R_y^k=\frac{4h^kR_0^kS_y^k}{S_0^k\left(1-h\right)+S_y^k(5h-1)}e^{-0.5\sigma_R^2+{\widetilde{R}}_y^k}\)` `\(S_y^k=\sum_{a}{\phi_{ik}N_{y,\gamma=female,a}^iw_{y,\gamma=female,a}^kE_a^k}\)` **Eqs 12, 13** + Density dependence spatial Bev-Holt at stock level `\(k\)` + SSB in `\(k\)` is summation over `\(i\)` in `\(k\)` (the magic of `\(\phi_{ik}\)`) --- # Reproduction II $R_y^i=\tau_{ik}R_y^k $ **Eq 15** + Recruitment happens at stock `\(k\)` and is partitioned into sub-area `\(i\)`. + Likely user-defined, by geographic area. --- # Reproduction III .large[ `\(R_y^k=\frac{4h^kR_0^kS_y^k}{S_0^k\left(1-h\right)+S_y^k(5h-1)}e^{-0.5\sigma_R^2+{\widetilde{R}}_y^k}\)` ] **Eq 12** + Steepness `\(h^k\)` .inverse[estimated with penalty/as hyper-parameter?] + RecDevs penalized with a .inverse[bias correction ramp?] --- # Discards `\({\Omega}_{y,\gamma,a}^f=\beta_3^{y,f,\gamma,a}\left(1+exp(-a-(\frac{\beta_1^{y,f,\gamma,a}+\beta_4^{y,f,\gamma,a}}{\beta_2^{y,f,\gamma,a}})\right)^{-1}\)` **Eq 16** + Discards *and* discard mortality are modeled... + .inverse[Thus discard input data are not pre-adjusted by mortality] + Such rates are fixed, but included in tuning of `\(F\)` --- # Retained Catches `\(C_y^{m,f}=\sum_{i\epsilon m}\sum_{\gamma}{\sum_{a}{\phi_{if}w}_{\gamma,a}^f\frac{s_{\gamma,a}^fF_y^f\mathrm{\Omega}_{y,\gamma,a}^f}{Z_{y,\gamma,a}^i}N_{y,\gamma,a}^i(1-e^{-Z_{y,\gamma,a}^i})}\)` **Eq 17** + Baranov (Ricker, 1975): catches occur by fleets `\(f\)` in sub-areas `\(i\)`, and accrue to mgmt regions `\(k\)`. + `\(\phi_{if}\)` determines whether or not `\(f\)` exploits `\(i\)` -- + `\(w^f_{\gamma,a}\)` .inverse[is fleet- and sex- specific weight-at-age for captured fish (assumed equivalent for all sub-areas i fished by f)] + Hybrid method used to tune `\(F\)` and generate `\(C_{pred}\)`, using total mortality (incl. discard, **Eqs 19:24**) --- # Survey Biomass --- ## Comps + .inverse[Aging Error] + .inverse[Expansions] + .inverse[Sample sizes estimated via Dirichlet-Multinomial?] --- # Reference Points --- ## Misc Questions ## [copied from Google Doc] + start year for whole model + aging error + expansions of comps, etc + data availability (by stock vs mgmt area) + treament of sample sizes -- dirichlet? + hyperparameters e.g. steepness, penalty on recdevs