model time step and species biology considerations for growth estimation in integrated stock...
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Model time step and species biology considerations for growth estimation in integrated stock assessments
P. R. Crone and J. L. ValeroSouthwest 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 designoSmall pelagic species example•Results•Conclusions•Further work
Model time step and growth estimationPresentation outline
•Underlying goalsoGeneral
Evaluate model dimension (time step) considerations for growth parameterization in integrated models
Contribute to good practices guidance for developing stock assessment modelsoSpecific
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 questionsoAre finer time steps necessary for modeling growth adequately in integrated fishery models?
oAre results from stock assessments sensitive to choice of time step?oDoes species’ life history strategy influence decisions for time step?
Growth estimation more sensitive for higher vs. lower productivity stocks?oH0: Estimated growth rate (K), abundance (SSBcurrent), … robust to choice of time step HA: Estimates sensitive to choice of time step
Model time step and growth estimationStudy motivation
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0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5
Length (cm)
Age (yr)
Fitch (1951)
Knaggs and Parrish (1973)
Crone et al. (2011)
P. mackerel - Length-at-age
• Biology / Ageing laboSpawning period (Mar-Oct)oSuccessive batch spawnero July 1st birthdateoModel year ≡ July - June• Changes in growth not evident• Can time-step choice mask
potential changes …?
Historical growth
•Strata ≡ speciesoHigh productivity (small pelagic spp. - P. mackerel example)oLow productivity (groundfish spp.)• Input factor ≡ model time stepoQuarteroSemesteroAnnual•Output variablesoQuantitative
VB growth parameter estimates (K, LAAmin and LAAmax, LAAmin_CV and LAAmax_CV)Management quantity estimates (SSBcurrent, MSY, depletion (SSBcurrent /SSBunfished)
oQualitativeModel complexity/speedFiner time steps smaller sample sizes for composition time series increased uncertaintyEvidence of model misspecification with related parameters (selectivity, M, spawner-recruit)
•Conduct simulations/estimations involving alternative model scenarioso 1 Operating model ≡ quarter time step (finest time-step model)o 3 Estimation models
Quarter, semester, annual time step
•ResultsoSummarize output and examine bias/precision of quantitative variables
Model time step and growth estimationStudy design
Annual time step Semester time step Quarter time step
LENGTH
AGE
COMPOSITIONS (1995-00)
AGE
Annual time step Semester time step Quarter time step
LENGTH
Len
gth
(cm
)
Age (yr)
Species
Quarter - Q
Simulated data sets100 replicates / time step
Estimation models (EM)
Assumed models
Operating model (OM)True model
Mackerel - M
Model time-step evaluationSimulation / estimation flow chart
annual - a MQa
MQqTime step
semester - s
quarter - q
MQs
Time step
Output
Growth estimates
Management estimates
K
LAAmin
LAAmax
LAAcv
MSY
SSBcurrent
Depletio
n
Compare EM output relative to OM results
𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒𝑒𝑟𝑟𝑜𝑟=( �̂�−𝜃)/𝜃
•Operating (true) model is simplified version of actual assessment oAge-structured model (Stock Synthesis) oQuarter time-step configuration serves as true modeloProduce simulated data sets (study replicates) with process erroroMonte Carlo resampling based on compositions (samples) and survey/CPUE
(CVs)• Estimation (assumed) models used to analyze replicatesoSimilar to operating model except for effects of input factoro Input factor ≡ time-step assumptions (quarter, semester, annual)oEach estimation model based on 100 replicates
• Limitations of operating model and conclusions drawn
Model time step and growth estimationOperating and estimation models
Model time step and growth estimationOperating and estimation models
MQq MQs MQaData
Sex CombinedCatch 1 FisheryIndex of abundance 1 CPUE, 1 SurveyBiological composition data Age 1 Fishery Mean length-at-age 1 Fishery
Dimensions/Parameterizations
Time period 1983-13
Time step Quarter Quarter Semester Annual
Growth (VB) Est Est Est
Natual mortality Fix Fix Fix
Selectivity (age-based, asymptotic, constant)
Fishery Est Est Est
Surveys Fix (mirror) Fix (mirror) Fix (mirror)
Spawner-recruit (recruits equally distributed) Est Est Est
P. mackerel OMEM
Model time step and growth estimationResults – Relative error plots
MQq MQs MQa MQq MQs MQa MQq MQs MQa
K LAAmin LAAmax
Rela
tive
err
or
Model time step and growth estimationResults – Relative error
Rela
tive
err
or
MQq MQs MQa MQq MQs MQa
LAAmin_CV LAAmax_CV
Model time step and growth estimationResults – LAA_CV estimates
LAAmin_CV LAAmax_CV
CV
MQq MQs MQa MQq MQs MQa
Model time step and growth estimationResults – Relative error plots
MQq MQs MQa MQq MQs MQa MQq MQs MQa
SSBcurrent MSYDepletion
Rela
tive
err
or
Model time step and growth estimationResults – Relative error plots
Growth↔Selectivity
MQq MQs MQa MQq MQs MQa
K Selectivity-at-age 1
Rela
tive
err
or
Model time step and growth estimationResults – Relative error plots
Time step↔Selectivity
Sele
ctiv
ity
Age
Selectivity-at-age 1
Rela
tive
err
or
MQq MQs MQa
Model time step and growth estimationConclusions
• QualitativeoStudy design appears useful for addressing research questions oModel complexity/speed not compromised in this example, but …oSample size limitations for some time periods with quarter time-step model
• QuantitativeoEstimate bias worse (to varying degrees) for broader time-step modelsoEstimate precision generally similar across time-step modelsoFor growth parameter estimates, bias differences between time-step models most
notable for K and less so for LAAmin, LAAmax
oFor growth estimate variability, bias differences between time-step models most notable for LAAmin and less so for LAAmax
oFor derived management quantities, bias differences between time-step models most notable for SSBcurrent, Depletion and less so for MSY
oUsual 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 estimationFurther work