Modeling fisheries and stocks spatially for Pacific Northwest Chinook salmon Rishi Sharma, CRITFC Henry Yuen, USFWS Mark Maunder, IATTC

Structure of Talk  Background  Life History and relationship to model  Estimating catch in Fisheries by stock.  Statistical Catch at Age Analysis (SCAA).  Adapting to a multi-stock framework.  Precision in Exploitation rates.  Wrap Up.

Background Jurisdiction. Fisheries. Value ($20-50 M/yr X-vessel price). Cost tagging and assessment ($15 M/yr).

Chinook Life Cycle Eggs, Fry & Juveniles Natural Spawning Escapement (Age 2, 3,4, 5,6) Ocean (Age 2,3,4,5, 6) Age 2 Ocean Recruits Maturation (% 2, 3, 4, 5) No Yes Nat Mortality Fresh water Ocean

Tag Data used in assessment

Escapement # of fish Life History (TIME) Cohort Analysis Population Total Fishery 3Fishery 4 Fishery 1 Fishery 2 Natural Mortality Catch Population ER = Population

ERROR Age 2 recruits Estimate Age 2 recruits SpawnersSpawners Ages 2,3,4,5 Maturation Estimated from tag data Catch (ocean) Ages 2,3,4,5 Catch (fresh water) Ages 2,3,4,5 Natural Mortality States of Nature (have a time dynamic) CURRENT VPA MODEL MECHANISM Projected By Cohort analysis estimates from a Base Set of Years CWT Based Size limit adjustments Projected By Cohort analysis estimates from a Base Set of Years CWT Based Size limit adjustments Spawners (Projected to equal Forecast & Observed Spawners over multiple ages, i.e. over the cohort)

Fresh water Ocean Age 2 recruits Estimate Age 2 recruits SpawnersSpawners Environmental Forcing functions Ages 2,3,4,5 Maturation estimated Catch (ocean) Ages 2,3,4,5 Catch (fresh water) Ages 2,3,4,5 Natural Mortality States of Nature (have a time dynamic) SCAA MODEL MECHANISM Catch (ocean) Projected Fn (abun, Vuln and Catchability, ocean) Effort Known Catch (f_water) Projected Fn (abun, Vuln and Catchability, Terminal) Effort Known Spawners (Projected) Fn (TR- Term_Catch)

Trade-Offs  Lesser assumptions.  Estimation framework.  Numerically intensive & Challenging.

Essential Approach Maximum Likelihood Estimation

Testing the Approach

Simulation Testing  Used a Ricker stock recruit with process error. Simulated different catchability, vulnerability and maturation schedules by different fisheries and time periods.  Estimated the recruitment deviates, and thereby age 2 recruitment.  Estimated vulnerability, catchability and maturation by time periods specified.  Ran 10,000 times (each run takes approximately 10 seconds-27 hours).

Spawner to age 2 recruit curve alpha beta Process Error ε~N(0,σ 2 ) a F=q a Es a Ocean Catch a Escapement a OBS Error SIMULATION MODEL compare Escapement a Ocean Catch a OBSERVATIONS WITH SIMULATED NOISE a Maturation a MODEL ESTIMATION a Terminal Catch a Age 2 Recruits a F=q a Es a Ocean Catch a a Terminal Catch a Escapement a a Terminal Catch a Escapement a a Maturation a Parameter Uncertainty 25 year time series

Summary of simulations  Model has a high accuracy on estimating Recruitment & Exploitation Rates.  Model is biased (underestimating) on true parameters on Catchability and Maturation.  The model does not appear to capture terminal vulnerability, though ocean vulnerability is marginally better.  Adding measurement error to the data, creates problems in estimation (lower error, CV 0.1)

4 Stock Model  Spatial variation in stocks modeled  Spatial variation in fisheries modeled  2 Pool Model structure.

1. S.E. Alaska 2. WCVI 3. Terminal WCVI 4. Terminal Fraser 5. Terminal Queets 6. Terminal Columbia Fisheries URB Lower Fraser WCVI Queets

4 stock- 4 fishery model  Parameters estimated: –Recruitment deviate over time (25 years X 4 stocks) –Selectivity (3-ages and 4 fishery over 3 time periods for 4 stocks =144) –Maturation (3 ages and 3 time periods=9*4=36) –Initial Cohort abundance (3*4=12) –Catchability by 3 time periods for 4 fisheries and 4 stocks=48 Total =350 parameters

Tricks to Make Model Converge  Maturation: Logistic by stock and time period (Prior)  Vulnerability: Logistic by stock, time period & fishery (Penalty).  Recruitment: Stock recruit functions by Area with time specific deviates (Prior).

Overall Model Fits by Stock

Recruitment

Selectivity By Age in SEAK

SEAK Exploitation

WCVI Selectivity

WCVI Exploitation

Terminal Selectivity

Terminal Exploitation

Incorporating Genetics  Using catch composition estimates.  Added to the Objective function using a Multinomial Likelihood.  Explicitly taking the values from Genetic Analysis.  Estimating proportions with assignment error within the model structure.

Summary  Spatially stocks and fisheries could be modeled in a single pool context using different selectivity curves over stocks, fisheries and time.  Model complexity trade-off.  Statistical catch at age models are more robust (empirical data and likelihood functions).  Can quantify the Uncertainty in our estimates, and use in predictive models.  Could add environmental forcing into the model.  Have the ability to incorporate genetic information.

Next Steps  Add genetics.  Stratify by gear.  Use age-length based estimates for selectivity by gear and area.  Add environmental covariates.  Quantify the scale at which fisheries and stocks could be aggregated for model.  Develop a migration module that connects fisheries and stocks.

Acknowledgements  Mike Matylewich (CRITFC) for supporting this project.  Henry Yuen (USFWS) & Mark Maunder (IATTC) for help with the ADMB coding, Robert Kope (NMFS) for initial review of the approach.  John Carlile (ADFG), & members of the Chinook Technical Committee (CTC-AWG).  NOAA for funding this research.