1. Richard Methot NOAA Fisheries Service Seattle, WA
Stock Synthesis: an Integrated Analysis Model to Enable Sustainable Fisheries
Richard Methot
NOAA Fisheries Service
Seattle, WA
I’m here to describe an integrated analysis model designed for the assessment data typically available for west coast groundfish and broadly applicable to a wide range of assessment situations.

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?

4. Stock Assessment Defined
Collecting, analyzing, and reporting demographic information to determine the effects of fishing on fish populations
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

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. STOCK ASSESSMENT PROCESS
CATCH
RETAINED AND
DISCARDED CATCH;
AGE/SIZE DATA
ABUNDANCE TREND
RESOURCE SURVEY
or FISHERY CPUE,
AGE/SIZE DATA
BIOLOGY
NATURAL MORTALITY,
GROWTH,
REPRODUCTION
ADVANCED MODELS
HABITAT
CLIMATE
ECOSYSTEM
MANMADE STRESS
POPULATION MODEL:
(Abundance, mortality)
SOCIOECONOMICS
FORECAST
Conceptually like NOAA Weather’s data assimilation models, but time scale is month/year, not hour/day
STOCK STATUS
OPTIMUM
YIELD

7. Fish Biology and Life History
Ease: Length & Weight >> Age > Eggs & Maturity >>> Mortality

8. Abundance Index Fishery-Independent Surveys

9. Source of Abundance Indexes
Each survey may support multiple assessments
Each assessment may use data from multiple surveys

10. 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

11. Commercial retained catch Commercial discard Recreational kept catch
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

12. To estimate total catch:
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

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
The general class of models termed Integrated Analysis incorporate a Population Model, an Observation Model, a Statistical Model, and a means to search for the best-fitting set of parameters
Generally, fishing mortality is treated as being separable into a age-specific selectivity and a year-specific level, but there are many permutations on this theme.

14. 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)

15. Age-Length Structured Population
Let’s explore the concept of length and age based modeling in more detail
The left panel shows the numbers at age in the population distributed across lengths according to the mean growth curve and population variance about this curve. I’ve put a larger, non-equilibrium number at age 5 to aid in the demonstration.
We’ll sample this population with this size-selectivity curve

16. Sampling & Observation Processes
With size-selectivity
And ageing imprecision
The result on the left is a size-selective sample of the population, the smallest fish are gone
Now we cannot exactly observe the real age of fish, Here on the right we see the catch at observed age is blurred along the age axis. Some misaged 5 year olds have inflated the apparent occurrence of 4 and 3 year olds.
What I’ve shown is a representation of actual processes at work to generate our data;
in order to assure unbiased results, we need to engineer these same processes into the model to generate expected values that are truly comparable to the data. We build the process into the model rather than attempt to transform the data.
The next step is to accumulate these expected values to either the length or the age’ axis.

17. Expected Values for Observations
Reminder in the upper left is the size selectivity
The lower left shows the size composition in the population and in the sample
The upper right shows the age composition in the population, in the sample, and as observed by our age determination process
Finally, the lower right shows the necessary consequences of these biologically realistic factors on mean size at age in the population, the sample and as observed by our age determination process

18. Discard & Retention

19. Integrates Time Series Estimation with Productivity Inference

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

21. Stock Synthesis Structure
NUMBERS-AT-AGE
Cohorts: gender, birth season, growth pattern;
“Morphs” can be nested within cohorts to achieve size-survivorship;
Distributed among areas
AREA
Age-specific movement between areas
FLEET / SURVEY
Length-, age-, gender selectivity
CATCH
F to match observed catch;
Catch partitioned into retained and discarded, with discard mortality
RECRUITMENT
Expected recruitment is a function of total female spawning biomass;
Optional environmental input;
apportioned among cohorts and morphs;
Forecast recruitments are estimated, so get variance
PARAMETERS
Can have prior/penalty;
Time-vary as time blocks, random annual deviations, or a function of input environmental data
So, let me recap SS2 structural features

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

25. 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

26. Graphical Interface: Toolbox

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
Today’s state-of-the-science advanced fishery assessment models work as dynamic simulations of the population process
An observation model derives expected values for the various kinds of available data.
Here I show the observed and predicted values for a triennial survey of relative population biomass (abundance). We get data like these from our fishery-independent surveys conducted on NOAA Fishery Survey Vessels and some chartered vessels.
I also show an example of the observed and predicted proportions-at-age for one year’s fishery catch. We get such data by sampling the fishery landings and determining ages of a subset of the fish.
Additional point:
An example of such a model is the Stock Synthesis program developed by NOAA fishery scientist Richard Methot and used for over 20 assessments in the Pacific region in 2005.

28. An Example
Simple vs. complex model structure
Time-varying model parameter
First, motivation for an advanced approach to catchability

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

32. 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

33. Results: all data, all parms, random walk q
Blue line = true values; red dot = estimate with 95% CI

34. Fishery q

35. CPUE only, Simple Model, constant q

36. Bias and Precision in Forecast Catch
Error bar is +/- 1 std error

37. NEXT STEPS Tier III Assessments Spatially explicit
Linked to ecosystem processes

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. Stock Assessment – Ecosystem Connection
TIME SERIES
OF RESULTS
BIOMASS,
RECRUITMENT,
GROWTH,
MORTALITY
SINGLE SPECIES
ASSESSMENT
MODEL
Tactical
SHORT-TERM
OPTIMUM
YIELD
LONG-TERM
INTEGRATED
ECOSYSTEM ASSESSMENT
CUMULATIVE EFFECTS OF FISHERIES AND OTHER FACTORS
Strategic
RESEARCH ON
INDICATOR
EFFECTS
INDICATORS
ENVIRONMENTAL,
ECOSYSTEM,
OCEANOGRAPHIC
SA model (whether Tier II or Tier III) produces time series of results
This time series is enough to forecast Optimum Yield, at least in the short-term (few years)
This time series also feeds into Holistic ecosystem model by providing information on changes in important ecosystem components
Results of the holistic ecosystem model can provide information on cumulative effects and interactions, thus ability to adjust long-term OY. But we are just beginning to attain this capability.
We also can make direct measurements of environmental factors and obtain some factors as results of ecosystem models.
These measurements alone are not enough to improve single-species asmt models.
There also needs to be applied research to determine plausible linkages between environmental factors (like ocean temperature) and assessment factors (like growth) that normally are assumed to be constant.
TWO-WAY

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 Recruitment
Annual random process with measurable outcome
Predictable from ecosystem and environmental factors
Growth & Reproduction
Measurable, but often held constant
Survey Catchability
Usually Constant or random walk
Linked to environmental factors
Natural Mortality
Mean level based on crude relationships and wishful thinking
Feasible?, or just wishful thinking on larger scale?

41. How Are We Doing?
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