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

0

5

10

15

20

25

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35

40

45

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