1. Current developments on steepness for tunas:
Shelton Harley
Pre-Assessment Workshop 4-8 April 2011, Noumea

2. Three part presentation
My presentation to the ISSF Steepness workshop
Outcomes from the ISSF steepness workshop
Preliminary meta-analysis of steepness in tunas

3. Outline Estimating steepness Meta-analysis
Modelling uncertainty in steepness
SR process for tropical tunas
Suggestions

4. h What we need Accurate estimates of spawners
Accurate estimates of recruits
Contrast in spawner abundance
Low recruitment variation

5. Estimating spawners
Definition of spawners - understanding the spawning process
Size based versus age-based processes?
Estimation of the spawning component – typically based on longline CPUE

6. Estimating recruits “Continuous” spawning
No ageing data and variable growth ... in space and time
Steepness
Recruitment variation
Moderate
Low
Very low

7. Our options – meta-analysis
Appropriate level of ‘integration’?
Need to incorporate estimation error in series
Assumptions of the underlying assessment s ..

8. Our options - uncertainty
Provide results across a range of assumed levels of steepness
How do we weight them?
How do we ‘really’ include uncertainty in steepness?

9. Uncertainty in steepness?
MSY=73,480mt
MSY=65,840mt
MSY=160,000mt
h=0.75
High SigmaR
h=0.75
Low SigmaR
Base model

10. A process for the relationship
Tuna are not salmon or reef fishes … where is the scope for density-dependence and compensation?
Tropical tunas spawn almost continuously when conditions are favorable (thought to be related to feed for condition and SST)
A process to maximize the time/space window for spawning – match/miss-match hypothesis?

11. Eggs and baskets
Aim to maximise the distribution of spawning in time and space
Reduced spawning biomass ... reduced time and space
Reduced probability of high recruitment and a higher probability of low recruitment
A variance-based process – expectations less relevant?

12. Mean or variance? More higher R at high SSB No apparent decline
in recruitment
variation
More lower R
at low SSB

13. Variation in recruitment
Recruitment variation typically higher at lower stock sizes in non-salmonid fishes
Opposite trend to the constant CV assumption
But … confounded with time and emergence of surface fisheries and improved size data

14. The “P” word
Does the Precautionary Approach have a place in assumptions about steepness?
Simulations suggest steepness most often over-estimated ..
Consequences – fishing effort too high and biomass reduced too low
Fishing strategies based on lower steepness – minimal lost yield, higher catch rates, and greater spatial extent of the stock
Is MSY a sensible concept for skipjack– in a deterministic sense?

17. Suggestions for a way forward
Direct ageing where possible
Research into meaningful estimates of spawning potential
Revisit meta-analyses as info improves
Don’t base stock assessment advice on a single estimate (or assumed value) of steepness
Projections should consider alternative assumptions of recruitment variation

18. ISSF Workshop

19. Summary of ISSF meeting
A workshop was held to examine two issues that significantly affect scientific management advice:
(1) Assumptions about the stock‐recruitment relationship, and
(2) Evaluating the implications of changing mortality on juvenile and small tuna
These issues are not always being treated consistently in tuna stock assessments

20. ISSF Workshop recommendations
That estimated values of steepness from individual assessments be treated with considerable caution. Analysts should evaluate the extent to which the stock--‐recruitment estimation or assumptions influence the estimates of recruitment;
RFMOs should collaborate towards undertaking a meta‐analysis of spawner‐recruitment data as initiated during this Workshop. It was recommended that analysts continue to develop this work with a view to provide further advice for the estimation of steepness in tuna assessments.

21. Continued
That stock status advice incorporate stock assessment structural and parameter uncertainty including a range of plausible steepness values;
That RFMO decision‐makers consider management measures and/or Harvest Control Rules that are robust to uncertainty in steepness, noting the precautionary approach and the economic benefits of maintaining stocks at higher stock sizes.
RFMOs should collaborate on methods for the incorporation of uncertainty of steepness into stock assessment advice, including approaches such as management strategy evaluation.

22. ISSF Other recommendations
The Workshop recommended that Fishery Impact plots be included routinely in tuna RFMO stock assessment reports.
The Workshop recommended that RFMOs facilitate meetings to compare the basic life history parameters being used in the tuna stock assessments, with a view to reconcile differences or improve consistency, if necessary.

23. ISSF results

24. SPC Preliminary analysis

25. Approach
Updating the analysis of Myers et al. (1999) Maximum reproductive rate of fish at low population sizes. CJFAS 56: 2404–2419.
Focus on estimating the slope at the origin (α) of a ‘standardised’ spawner recruitment curve – both point estimates and likelihood profiles.
Translate into ‘steepness’

26. Models
Ricker:
Beverton-Holt:

27. Need to standardize ..
Convert recruits into replacement spawners using the spawning biomass per recruit in the absence of fishing
So that

28. And then to steepness
represents the number of spawners produced by each spawner over its lifetime at very low spawner abundance, i.e., assuming absolutely no density dependence.
Steepness is:

29. Data sets Albacore tuna Bigeye tuna Bluefin tuna Skipjack
North Atlantic
North Pacific
South Pacific
Bigeye tuna
Atlantic
Indian Ocean
WCPO
Bluefin tuna
Eastern Atlantic
Skipjack
WCPO
Yellowfin tuna
Indian Ocean

30. Individual fits

31. Individual fits Stock Ricker BH ALB_AT 0.73 0.96 ALB_NP 0.79 1.00
ALB_SP
0.37
0.45
BET_AT
0.77
BET_IO
0.94
0.95
BET_WP
0.90
BFT_EA
0.80
SKJ_WP
0.78
YFT_IO
0.60
0.64
YFT_WP
0.70
0.81

32. The meta-analysis
A random effect meta-analysis undertaken using nlme() in R
Basic model repeated for RK and BH:
Also estimate BLUP
Transform back into steepness ‘space’

33. Preliminary results - BLUPs

34. Preliminary results - Priors

35. Next steps Data Methods Potential ISSF support
Refine data set – appropriate model runs
Increase number of stocks
Methods
nlme() …. Have there been improvements since 1999
Incorporation of estimation error in recruitment time series
Incorporation of structural uncertainty – multiple assessment runs
Broken-stick model potential application
Potential ISSF support

36. Initial recommendations
Either fix steepness at the mode of the Ricker model based RE distribution
Or fix steepness at a range of values and derive a ‘point estimate’ for stock status weighting the values based on the RE distribution