1. Catch at age table: lots of work, lots of data and apparent information

2. A bit of history Fry 1940s: ”virtual population”, “catch curve”
Gulland 1950: VPA (virtual population analysis)
Doubleday, Paloheimo : SCA (statistical catch at age analysis)
Deriso, Fournier : SCA with auxiliary information
Kimura 1982: “stock reduction analysis”
Gavaris 1979: ADAPT program for VPA
Fournier 1990: ADMB for faster SCA
Methot 1990: “stock synthesis” (SCA plus)

3. Parameter estimation and state reconstruction for dynamic models
Observation
errors
Process
errors
Parameters
Observation
Model
(predicted y)
Data
(observed y)
State dynamics
Model N
Statistical
criterion y N
Nt+1=Nt-Ct
yt=qNt
Parameter No
Parameter q
Log-likelihood function

4. Catch at age table effects
Cohort effect
Age
effect
Year effect

5. And there can be so much nice data (as for Newfoundland cod)

6. Where do you get the Cat? Age composition sampling (best)
Age composition by length, expansion of length frequencies using that composition (OK if good composition data at all lengths)
Age-length “key” (assign each length in length frequency data to an age) (Bad!)
Predict length composition directly (Synthesis type models only) (Very bad unless GTG accounting used for size structure)

7. What’s the matter with good old catch curves?
Z=0.52
-Assume older ages equally vulnerable (why are there less old fish?)
-Only use information in data from “fully recruited” (equally vulnerable) ages
-Ignore effects of changes in recruitment (again, why are there less
old fish?)
-Assume same harvest impact in all past years

8. Two ways to parameterize catch at age models (SCA vs VPA)
VPA: backward in time
Na,t=Na+1,t+1/S+Ca,t
Problem: how to get the U’s along the edge of the table, to set N=C/U?
SCA: forward in time
Na+1,t+1=Na,t(1-Uat)S Ca,t=Utva,tNa,t
Problem: too many parameters
R1 R2 R3…………………Rn
C1/U1
C2/U2 C3/U3…
Cm/Um
N2 N3… Nm
Cn/U1 Cn/U2 Cn/U3…Cn-1/Un

9. Deciding between SCA and VPA
DON’T DECIDE. When you can, use both (can’t use VPA except over periods where catch at age can be estimated for every historical year)
SCA more precise and accurate when fishery has had stable, simple logistic vulnerability at age pattern (SCA predicts catch at age, so “sees” F effects in data)
But SCA can be badly biased when vulnerability schedule has changed a lot and/or is dome-shaped (F effects in catch at age data confounded with vulnerability changes)
Use VPA whenever possible to check for complex, changing vulnerability patterns

10. Common causes of severe biases in estimated stock size and trend
Bad abundance index data (especially hyperstable cpues)
Rapid changes in size selectivity (especially targeting small fish as stock declines, makes recruitment appear high)
Inappropriate priors for recruitment variation when recruitment “constrained” to vary around a stock-recruitment curve
Dome-shaped vulnerability (makes F look too high when ignored, and too low when estimated but estimates are confounded with effects of F or recruitment trends on proportions of older fish

11. But sometimes they are still very useful, as for Vaughan’s menhaden data
How could Z have decreased while effort
was Increasing?

12. Output control and age-structured assessments don’t mix well?
Shelton, ICES J. Mar. Sci. (2007); note increases in F (circles) as stock size declined in range-contracting stocks. Shelton notes that scientific advice is not being consistently followed, even when that advice is not biased by assessment problems for range-contracting stocks.