Model time step and species biology considerations for growth estimation in integrated stock assessments P. R. Crone and J. L. Valero Southwest Fisheries Science Center (NOAA) Center for the Advancement of Population Assessment Methodology (CAPAM) 8901 La Jolla Shores, Dr., La Jolla, CA 92037, USA

Study motivation Study design o Small pelagic species example Results Conclusions Further work Model time step and growth estimation Presentation outline

Underlying goals o General Evaluate model dimension (time step) considerations for growth parameterization in integrated models Contribute to good practices guidance for developing stock assessment models o Specific Ongoing sensitivity analysis with small pelagic species assessment models used for advising management Merits/drawbacks of using more straightforward assessment model to meet management objective Research questions o Are finer time steps necessary for modeling growth adequately in integrated fishery models? o Are results from stock assessments sensitive to choice of time step? o Does species’ life history strategy influence decisions for time step? Growth estimation more sensitive for higher vs. lower productivity stocks? o H 0 : Estimated growth rate (K), abundance (SSB current ), … robust to choice of time step H A : Estimates sensitive to choice of time step Model time step and growth estimation Study motivation

Biology / Ageing lab o Spawning period (Mar-Oct) o Successive batch spawner o July 1 st birthdate o Model year ≡ July - June Changes in growth not evident Can time-step choice mask potential changes …? Historical growth

Strata ≡ species o High productivity (small pelagic spp. - P. mackerel example) o Low productivity (groundfish spp.) Input factor ≡ model time step o Quarter o Semester o Annual Output variables o Quantitative VB growth parameter estimates (K, LAA min and LAA max, LAA min _CV and LAA max _CV) Management quantity estimates (SSB current, MSY, depletion (SSB current /SSB unfished ) o Qualitative Model complexity/speed Finer time steps  smaller sample sizes for composition time series  increased uncertainty Evidence of model misspecification with related parameters (selectivity, M, spawner-recruit) Conduct simulations/estimations involving alternative model scenarios o 1 Operating model ≡ quarter time step (finest time-step model) o 3 Estimation models Quarter, semester, annual time step Results o Summarize output and examine bias/precision of quantitative variables Model time step and growth estimation Study design

Annual time step Semester time stepQuarter time step LENGTH AGE COMPOSITIONS ( ) AGE Annual time stepSemester time stepQuarter time step LENGTH Length (cm) Age (yr)

Species Q uarter - Q Simulated data sets 100 replicates / time step Estimation models (EM) Assumed models Operating model (OM) True model M ackerel - M Model time-step evaluation Simulation / estimation flow chart a nnual - a MQa MQq Time step s emester - s q uarter - q MQs Time step Output Growth estimates Management estimates K LAA min LAA max LAA cv MSY SSB current Depletion Compare EM output relative to OM results

Operating (true) model is simplified version of actual assessment o Age-structured model (Stock Synthesis) o Quarter time-step configuration serves as true model o Produce simulated data sets (study replicates) with process error o Monte Carlo resampling based on compositions (samples) and survey/CPUE (CVs) Estimation (assumed) models used to analyze replicates o Similar to operating model except for effects of input factor o Input factor ≡ time-step assumptions (quarter, semester, annual) o Each estimation model based on 100 replicates Limitations of operating model and conclusions drawn Model time step and growth estimation Operating and estimation models

Model time step and growth estimation Operating and estimation models

Model time step and growth estimation Results – Relative error plots MQqMQsMQa MQq MQsMQa MQqMQs MQa K LAA min LAA max Relative error

Model time step and growth estimation Results – Relative error Relative error MQq MQs MQa MQq MQs MQa LAA min _CVLAA max _CV

Model time step and growth estimation Results – LAA_CV estimates LAA min _CV LAA max _CV CV MQq MQs MQa MQq MQs MQa

Model time step and growth estimation Results – Relative error plots MQqMQsMQa MQqMQsMQa MQqMQsMQa SSB current MSY Depletion Relative error

Model time step and growth estimation Results – Relative error plots Growth↔Selectivity MQq MQsMQa MQq MQs MQa KSelectivity-at-age 1 Relative error

Model time step and growth estimation Results – Relative error plots Time step↔Selectivity Selectivity Age Selectivity-at-age 1 Relative error MQq MQs MQa

Model time step and growth estimation Conclusions Qualitative o Study design appears useful for addressing research questions o Model complexity/speed not compromised in this example, but … o Sample size limitations for some time periods with quarter time-step model Quantitative o Estimate bias worse (to varying degrees) for broader time-step models o Estimate precision generally similar across time-step models o For growth parameter estimates, bias differences between time-step models most notable for K and less so for LAA min, LAA max o For growth estimate variability, bias differences between time-step models most notable for LAA min and less so for LAA max o For derived management quantities, bias differences between time-step models most notable for SSB current, Depletion and less so for MSY o Usual suspect (selectivity) interacts with time-step assumptions and contributes to increased uncertainty for abundance estimates  Increasing length of time step → slower growth → higher probability of capture-at-age 1

Lower productivity species (e.g., some groundfish assessments) Recruitment apportionment (assumptions) across time-steps (different fixed scenarios and estimated) Sample size considerations regarding composition time series Model performance for species/assessments associated with length-based/age- structured models (e.g., most tuna assessments) Identify other areas of potential data conflict/parameter tension in assessment model Model time step and growth estimation Further work