Overview of BSAI Pacific Ocean Perch Model Structure and Recent Developments

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The BSAI Pacific Ocean Perch assessment model has evolved over the years, with a history dating back to pre-2000. Recent developments include the combination of separate models for AI and EBS, adjustments to age error matrices, and enhancements in handling composition data. The model structure focuses on recruitment, annual deviations, and initial abundance parameters. These advancements have improved the accuracy and robustness of the assessment model for Pacific Ocean Perch in the BSAI region.

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2022 BSAI Pacific ocean perch Model Structure and Results

BSAI POP Outline 1) History of assessment 2) Recent model changes 3) Model structure 4) Model likelihoods 5) Parameter estimates 6) Data fits 7) Retrospective results, and uncertainty U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 1

History of assessment models Prior to 2000: stock synthesis Current model based on forward projecting population model, with separable fishing mortalities Coded in ADMB, similar to many other AFSC models: 1) AMAK; 2) Courtney et al. 2007; 3) GOA POP model U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 2

Recent model developments 2001: Combined BSAI model (previously separate models for AI and EBS) 2006: Prior distributions are used for natural mortality and AI survey catchability 2012: Increased plus group from 25 to 40 years 2012: Maturity curve estimated within the model 2012: Aging error matrix adjusted to account for ageing errors within plus group 2014: Bicubic spline for fishery selectivity 2014: Extended ageing error matrix U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 3

Recent model developments (continued) 2016: McAllister-Ianelli iterative reweighting of age/length composition data 2016: EBS slope survey biomass and composition data used in assessment U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 4

Model Structure U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 5

Model Structure: Numbers at age Recruitment (age 3) ? ?2,?= ???+?? Parameters: Mean recruitment: log-scale, freely estimated Annual recruitment deviations: log-scale, constrained by recruitment variability ( r) Initial abundance ??,1960= ?????? ? 3 ? ??+,1960= ?????? ?+ 3 ?/ 1 ? ? Parameters Initial recruitment for unfished population, equilibrium population assumption U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 6

Model Structure: Numbers at age Annual numbers at age ??,?= ?? 1,? 1? ?+?? 1,? 1= ?? 1,? 1? ?? 1,? 1 Parameters: Natural mortality: log-scale, constrained with prior penalty Fishing mortality Plus group numbers ??+,?= ??+ 1,? 1? ??+ 1,? 1+ ??+,? 1? ??+,? 1 Spawning biomass ?+ ?? ????,?? ??,? ??_???? ???= ?=3 U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 7

Model Structure: Catch Annual Catch ??= ?+ ??,???,?1 ? ??,? ??,? ?? Parameters: Fishing mortality ?=3 Annual Fishing Mortality ? ???= ??,? ????+?? ??,?= ??,? Parameters Fishing selectivity Mean fishing mortality: log-scale, freely estimated Fishing mortality deviations: log-scale, constrained with penalty U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 8

Model structure: Fishery selectivity ADMB function bicubic_spline bicubic_spline(scal_yr_nodes, scal_age_nodes, sel_par, log_sel_fish); 2010 Based in code from Numerical Recipes (Press et al 1992) 2000 location where selectivity is interpolated 1990 knot locations Year 1980 1970 1960 0 10 20 30 40 Age Methods for controlling smoothness 1) Number of knots (I use 5 for age and 5 for year) 2) First derivative across ages (descending only; controls dome-shapeness) 3) Second derivative across ages (controls smoothness) 4) First and second derivatives across years U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 9

Model structure: Survey index Aleutian Islands bottom trawl survey ?+ ??= ????? ??? ??,??? ?=3 Eastern Bering Sea slope bottom trawl survey ?+ ??= ??????? ??? ??,??? ?=3 Parameters Survey selectivity (q): estimated on log-scale, with prior Survey selectivity (logistic) Proportion of biomass in survey area ( ) U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 10

Model structure: Composition data Bottom trawl survey age ? ??,??? ?=3 ? ??,? = ?? ? ?+??,??? ? Fishery age ??,? ?+ ? ??,? = ?? ? ?? ?=3 Fishery length ??,? ?+ ?= ?? ? ??,? ??,? ?=3 U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 11

Model structure: Parameters Estimated within the model: Parameter type 1) Fishing mortality mean 2) Fishing mortality deviations 3) Recruitment mean 4) Recruitment deviations 5) Unfished recruitment 6) Biomass survey catchabilities 7) Fishery selectivity parameters 8) Survey selectivity parameters 9) Natural mortality rate 10) Maturity parameters Total parameters Number 1 61 1 58 1 2 25 4 1 2 156 U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 12

Model structure: parameters Estimated outside the model Parameter type Von Bertalanffy length at age parameters Weight at length parameters SD in length with age (polynomial) Aging error (linear) Proportion of stock in survey subareas Number 3 2 5 2 1 U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 13

Model Likelihoods U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 14

Model Likelihoods: Fitted data Catch: ? ?= 500, ? = 0.0001 2 ??+ ? ??+ ? ? ?= ? ? ln ? Bottom trawl survey biomass: CV = Coefficient of variation for survey biomass estimate 2 ?? ?? 1 ? ?= 2ln 2 ???,? ? U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 15

Model Likelihoods: Fitted data Age and length compositions (fishery and survey): ??,? is a reweighted sample size ? ? ? ? ? ?? ? = ??,? ??,? ln ??,? + ? ? ? Input sample sizes are the square root of the number of observations, and this is reweighted with the McAllister-Ianelli procedure. U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 16

Model Likelihoods: Fitted data Maturity at age: Binomial distribution, with two data sets. ????= ?? ??,??? ? + ??,? ??,? 1 ln(? ? ? D = dataset, n = number of fish observed, y = number of mature fish observed, = estimated proportion maturity by age. The weights ( ) can differ by age to allow sensible fits at low ages U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 17

Model Likelihoods: Priors/penalties Prior parameter penalty 2 1 ? ??= 2ln ?????? 2?? Natural Mortality 0.05 0.05 AI survey catchability 1.0 0.45 Prior Prior CV U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 18

Model Likelihoods: Priors/penalties Recruitment deviations ?+ ?ln?? ??= ?? ? Fishing mortality deviations: ??= 0.1 ? ??= ?? ?? ? U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 19

Data weighting General approach is that the second stage sample sizes ( ) are the product of a first stage sample sizes ( ) and a weight y j N, N, ~ j y ~ = N w N , , j y j j y A single weight for each data type (j) The weights are updated with each model run, and iterated until they converge U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 20

Data weighting McAllister-Ianelli (method TA1.1 in Francis 2011) Weight by the average ratio of effective sample size to the stage 1 sample size U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 21

Model Results U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 22

Results Recuitment Fishing mortality Fishing selectivity Bottom trawl selectivity, catchability Comparison of previous values Natural mortality Parameter CVs CVs on total and spawning biomass U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 23

Model Results: Recruitment U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 24

Model Results: Recruitment Estimated mean log recruitment = 4.32 U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 25

Model Results: Fishing mortality U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 26

Model Results: Fishery selectivity U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 27

Model Results: Bottom trawl survey selectivity Eastern Bering Sea (red), Aleutian Islands (black) U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 28

Model Results: Bottom trawl survey catchability AI catchability has been ~ 1.3 U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 29

Model Results: Bottom trawl survey catchability Other studies U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 30

Model results: natural mortality 2020 assessment estimate: 0.056 0.07 0.06 Survey Cathability 0.05 0.04 0.03 0.02 0.01 0 2008 2010 2012 Assessment Year 2014 2016 2018 2020 U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 31

Model Results Data fits U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 32

BSAI fishery age composition U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 33

Pearson residuals fishery age comps Blue is positive, red is negative U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 34

Fishery length composition U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 35

Pearson residuals fishery length comps Blue is positive, red is negative U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 36

AI survey age composition U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 37

Pearson residuals AI survey age comps Blue is positive, red is negative U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 38

EBS survey age composition Not a great fit to the EBS survey age compositions 2000 year class is strong in the AI age data, not so much in the EBS data U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 39

Pearson residuals EBS survey age comps Blue is positive, red is negative U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 40

Fit to the AI survey U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 41

Fit to the EBS survey index U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 42

Model Results Derived variables, and management reference points U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 43

Total and Spawning biomass U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 44

Phase plane plot U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 45

Projected SSB U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 46

Model Results Diagnostics (Retrospective analysis, likelihood profiles) Uncertainty Parameter correlations U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 47

BSAI POP retrospective pattern Mohn s rho = -0.24 (-0.45 in 2018 assessment) U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 48