Stock Synthesis:an Integrated Analysis Model
to Enable Sustainable Fisheries
Richard MethotNOAA Fisheries
ServiceSeattle, WA
2
OUTLINE
• Management Needs• Stock Assessment Role• Data Requirements• Stock Synthesis• Some Technical Advancements• Getting to Ecosystem
3
Control Rules, Status Determinations
and Operational Models•Is stock overfished or is overfishing occurring?
•What level of future catch will prevent overfishing, rebuild overfished stocks and achieve optimum yield?
ABUNDANCE (BIOMASS)
AN
NU
AL
CA
TC
H
BmsyBlimit
Overfished
Overfishing Catch Limit
Catch Target
4
Stock Assessment Defined
• Simplest System–Link control rule to simple data-based indicator of trend in B or F
–Easy to communicate; assumptions are buried
–Hard to tell when you’ve got it wrong
–Hard to put current level in historical context
• Full Model– Estimate level,
trend and forecast for abundance and mortality to implement control rules
– Cross-calibrates data types
– Complex to review and communicate
– Bridges to integrated ecosystem assessment
Collecting, analyzing, and reporting demographic information to determine the effects of fishing on fish populations
5
Idealized Assessment System
• Standardized, timely, comprehensive data
• Standardized models at the sweet spot of complexity
• Trusted process thru adequate review of data and models
• Timely updates using trusted process
• Clear communication of results, with uncertainty, to clients
6
POPULATION MODEL:(Abundance, mortality)
POPULATION MODEL:(Abundance, mortality)
STOCK STATUSSTOCK STATUS OPTIMUM YIELD
OPTIMUM YIELD
CATCHRETAINED AND
DISCARDED CATCH;AGE/SIZE DATA
BIOLOGY NATURAL MORTALITY,
GROWTH, REPRODUCTION
ABUNDANCE TREND RESOURCE SURVEY
or FISHERY CPUE,AGE/SIZE DATA
ADVANCED MODELS HABITAT CLIMATE ECOSYSTEM MANMADE STRESS
SOCIOECONOMICS
STOCK ASSESSMENT PROCESS
Conceptually like NOAA Weather’s data assimilation models, but time scale is month/year, not hour/day
7
Fish Biology and Life History
0 5 10 15 20 25
AGE
Length
Weight
Eggs
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 5 10 15 20 25
AGE
% Mature
Natural Mortality
Ease: Length & Weight >> Age > Eggs & Maturity >>> Mortality
9
Source of Abundance Indexes
Each survey may support multiple assessmentsEach assessment may use data from multiple surveys
Catch: What’s Been Removed
• Must account for all fishing mortality– Commercial and recreational– Retained and discarded– Discard survival fraction
• Model finds F that matches observed catch given estimated population abundance– Because catch is nearly always the most
complete and most precise of any other data in the model
– But also possible to treat catch as a quantity that is imprecise and then to estimate F as a parameter taking into account the fit to all types of data
10
Catch Components
• Commercial retained catch– fish ticket census
• Commercial discard– observer program
• Recreational kept catch– catch/angler trip x N angler trips
• Recreational releases– Interview x N angler trips
11
Catch per Unit Effort
• To estimate total catch:– Catch = CPUE x Total Effort– So CPUE must be effort weighted
• As an index of population abundance– Relative biomass index = CPUE x
stock area– So CPUE must be stratified by area
so heavily fished sites are not overly weighted
12
13
Integrated Analysis Models
• Population Model – the core
– Recruitment, mortality, growth
• Observation Model – first layer
– Derive Expected Values for Data
• Likelihood-based Statistical Model – second layer
– Quantify Goodness-of-Fit
• Algorithm to Search for Parameter Set that Maximizes the Likelihood
• Cast results in terms of management quantities
• Propagate uncertainty in fit onto confidence for management quantities
Stock Synthesis History
• Anchovy synthesis (~1985)• Generalized model for west coast
groundfish (1988)• Complete re-code in ADMB as SS2
(2003)• Add Graphical Interface (2005)• SS_V3 adds tag-recapture and
other features (2009)
14
15
Age-Length Structured Population
60
52
46
40
34
28
22
16
10
1
3
5
7
9
11
13
15
17
20
22
SIZE
AGE
POPULATION
0.0
0.2
0.4
0.6
0.8
1.0
25 30 35 40 45
SIZE
SE
LE
CT
IVIT
Y
16
Sampling & Observation Processes
60
52
46
40
34
28
22
16
10
1
3
5
7
9
11
13
15
17
19
21
23
SIZE
AGE
CATCH AT TRUE AGE
60
52
46
40
34
28
22
16
10
1
3
5
7
9
11
13
15
17
19
21
23+
SIZE
AGE'
CATCH-AT-OBSERVED "AGE"
With size-selectivity
And ageing imprecision
17
Expected Values for Observations
10 20 30 40 50 60
SE
LE
CT
IVIT
Y
SIZE
10 20 30 40 50 60
FR
EQ
UE
NC
Y
SIZE
POPULATIONCATCH
0 5 10 15 20 25
FR
EQ
UE
NC
Y
AGE
POPULATION
CATCH AT TRUE AGE
CATCH AT OBSERVED AGE
0 5 10 15 20 25
SIZ
E-A
T-A
GE
AGE
SIZE-at-TRUE AGE (population)
SIZE-at-TRUE AGE (catch)
SIZE-at-OBS AGE (catch)
18
Discard & Retention
0.0
0.5
1.0
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0 20 40 60 80 100
Re
ten
ton
Fre
qu
en
cy
Size
Retained-obs
Retained-est
Discard-obs
Discard-est
Frac. Retained
19
Integrates Time Series Estimation with Productivity
Inference
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0 5000 10000 15000 20000 25000 30000 35000 40000
Female Spawning Biomass
Rec
ruit
men
t
ExpectedBias-adjustTime_seriesVirgin & Init
20
Integrated Analysis
• Produces comprehensive estimates of model uncertainty
• Smoothly transitions from pre-data era, to data-rich era, to forecast
• Stabilizing factor:– Continuous population dynamics process
0
5000
10000
15000
20000
25000
30000
35000
40000
1950 1970 1990 2010YEAR
Biomass
Forecast
Catch DataOnly
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
50000
1950 1970 1990 2010YEAR
Recruitment
21
AREAAge-specific movement between areas
FLEET / SURVEYLength-, age-, gender selectivity
NUMBERS-AT-AGECohorts: gender, birth season, growth pattern;“Morphs” can be nested within cohorts to achieve size-survivorship;Distributed among areas
RECRUITMENTExpected recruitment is a function of total female spawning biomass;Optional environmental input;apportioned among cohorts and morphs;Forecast recruitments are estimated, so get variance
Stock Synthesis Structure
CATCHF to match observed catch;Catch partitioned into retained and discarded, with discard mortality
PARAMETERSCan have prior/penalty;Time-vary as time blocks, random annual deviations, or a function of input environmental data
22
Stock Synthesis Data
• Retained catch• CPUE and survey
abundance
• Age composition– Within length range
• Size composition– By biomass or numbers– Within gender and
discard/retained– Weight bins or length
bins
• Mean length-at-age
• % Discard• Mean body
weight• Tag-recapture• Stock
composition
23
Variance Estimation
• Inverse Hessian (parametric quadratic approximation)
• Likelihood profiles• MCMC (brute force, non-
parametric)• Parametric bootstrap
24
Risk Assessment
– Calculate future benefits and probability of overfishing and stock depletion as a function of harvest policy for each future year
– Accounting for:•Uncertainty in current stock abundance•Variability in future recruitment•Uncertain estimate of benchmarks•Incomplete control of fishery catch•Time lag between data acquisition and mgmt revision
•Model scenarios•retrospective biases•Pr(ecosystem or climate shift)•Impacts on other ecosystem components
ADMB
• Auto-Differentiation Model Builder
• C++ overlay developed by Dave Fournier in 1980s
• Co-evolved with advancement of fishery models
• Recently purchased by Univ Cal (NCEAS) using a private grant
• Now available publically and will become open source software
25
27
Stock Synthesis Overview• Age-structured simulation model of population
– Recruitment, natural and fishing mortality, growth
• Observation sub-model derives expected values for observed data of various kinds and is robust to missing observations– Survey abundance, catch, proportions-at-age or length
• Can work with limited data when flexible options set to mimic simplifying assumptions of simple models
• Can include environmental covariates affecting population and observation processes
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
200000
1974 1984 1994 2004
YEAR
SU
RV
EY
BIO
MA
SS
OBS +- 2 se
PREDICT
FISHERY AGE COMP in 1995
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15-19
20-24
25+
AGE
FR
AC
TIO
N
OBSERVE
PREDICT
An Example
• Simple vs. complex model structure
• Time-varying model parameter• First, motivation for an
advanced approach to catchability
28
29
Calibrating Abundance Index
•The observed annual abundance index, Ot, is basically density (CPUE) averaged over the spatial extent of the stock
•Call model’s estimate of abundance, At
•In model: E(Ot) = q x At + e•Where q is an estimated model parameter•Concept of q remains the same across a range of data scenarios:
30
Calibrating Abundance Index
•If O time series comes from a single Fisheries Survey Vessel
•If survey vessel A replaces survey B and a calibration experiment is done
•If O come from four chartered fishing vessels each covering the entire area
•If O come from hundreds of fishing vessels using statistical model to adjust for spatial and seasonal effort concentration
31
Abundance Index Time Series
•Each set-up is correct, but what’s wrong with the big picture?
•q is not perfectly constant for any method!
•Some methods standardize q better than others
•Building models that admit the inherent variability in qt and constrain q variability through information about standardization and calibration can:
– achieve a scalable approach across methods;
– incorporate q uncertainty in overall C.I.;– Show value of calibration and
standardization
Example
• Fishery catch• CPUE, CV=0.1,
density-dependent q
• Triennial fishery-independent survey, CV=0.3
• Age and size composition, sample size = 125 fish
32
1970 1980 1990 2000
Catch
Survey
Fishery_CPUE
Results:all data, all parms, random walk
q
0.0
0.1
0.2
0.3
0.4
1970 1990 2010YEAR
F. Mort
0
2000
4000
6000
8000
10000
12000
1970 1990 2010YEAR
Catch
0
5000
10000
15000
20000
25000
30000
35000
40000
1950 1970 1990 2010YEAR
Biomass
Forecast
Catch DataOnly
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
50000
1950 1970 1990 2010YEAR
Recruitment
Blue line = true values; red dot = estimate with 95% CI
Fishery q
34
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
1975 1985 1995
CATC
HA
BILI
TY (q
)
YEAR
True q
Random walk estimated q
CPUE only, Simple Model, constant q
0.0
0.1
0.2
0.3
0.4
1970 1990 2010YEAR
F. Mort
0
2000
4000
6000
8000
10000
12000
14000
1970 1990 2010YEAR
Catch
0
10000
20000
30000
40000
50000
60000
70000
80000
1950 1970 1990 2010YEAR
Biomass
Forecast
Catch DataOnly
0
5000
10000
15000
20000
25000
30000
35000
1950 1970 1990 2010YEAR
Recruitment
Bias and Precision in Forecast Catch
36
0
2000
4000
6000
8000
10000
12000
14000
TRUE All data, all parm, randwalk
All data, all parm,
constant q
Only CPUE, all parms,
constant q
Only CPUE, few parm, equil recr, constant q
Catc
h in
200
1
Error bar is +/- 1 std error
38
Space: The Final Frontier
• “Unit Stock” paradigm:– Sufficient mixing so that localized
recruitment and mortality is diffused throughout range of stock
– Spatially explicit data is processed to stock-wide averages
• Marine Protected Area paradigm:– Little mixing so that protected fish stay
protected• Challenge: Implement spatially
explicit assessment structure with movement and without bloating data requirements
39
OPTIMUM YIELD
OPTIMUM YIELD
SINGLE SPECIESASSESSMENT
MODELTactical
TIME SERIESOF RESULTS
BIOMASS,RECRUITMENT,
GROWTH,MORTALITY
Stock Assessment – Ecosystem Connection
INTEGRATEDECOSYSTEM
ASSESSMENT CUMULATIVE EFFECTS OF
FISHERIES AND OTHER FACTORS
Strategic
INDICATORS ENVIRONMENTAL,ECOSYSTEM,OCEANOGRAPHIC
RESEARCH ONINDICATOR
EFFECTS
40
Getting to Tier III
Process Tier II Tier III
Average Productivity(Spawner-Recruitment)
Empirical over decades of fishing
Predict from Ecosystem Food Web and Climate Regimes
Annual RecruitmentAnnual random process with measurable outcome
Predictable from ecosystem and environmental factors
Growth & ReproductionMeasurable, but often held constant
Predictable from ecosystem and environmental factors
Survey CatchabilityUsually Constant or random walk
Linked to environmental factors
Natural MortalityMean level based on crude relationships and wishful thinking
Feasible?, or just wishful thinking on larger scale?
41
How Are We Doing?
YearAssessments
DoneStocks withAdeq. Asmt.
2000 37 1062001 53 1112002 64 1062003 60 1072004 63 1082005 105 1202006 68 1202007 74 128
Assessments of 230 FSSI stocks following SAIP and increased EASA funds
42
Summary
Stock Synthesis Integrated Analysis Model
• Flexible to accommodate multiple fisheries and surveys
• Explicitly models pop-dyn and observation processes (movement, ageing imprecision, size and age selectivity, discard, etc.)
• Parameters can be a function of environmental and ecosystem time series
• Estimates precision of results• Estimates stock productivity, MSY and
other management quantities and forecasts