1. 11/19/2018
Day 3 Session 3 Special Session – Uncertainty, the stock recruitment relationship and “steepness”

2. 11/19/2018
Session overview
As we have seen over the past day or so, one of the most significant and common sources of uncertainty in all of the tuna stock assessments is the steepness of the stock recruitment relationship.
We have discussed this in previous workshops during the “Recruitment” sessions. However this issue is becoming a major focus of discussion in both the SC but also globally.
Recently, there was a large international meeting of scientists which was devoted to the discussion of this problem……How to estimate steepness?

3. 11/19/2018
Session overview
Because this is likely to be, once again, a topic of discussion at the upcoming SC7 meeting, we thought it timely to:
Briefly review what we have previously learnt about the stock recruitment relationship and steepness, as a lead in to discussions of,
Current scientific efforts to find ways to more accurately estimate steepness, and thereby significantly reduce the uncertainty currently inherent to most tuna stock assessments

4. What is Recruitment? Biomass We all know what recruitment is:
11/19/2018
Bt+1=Bt+R+G-M - C
What is Recruitment?
We all know what recruitment is:
“The number of fish alive at a specified stage after hatching (e.g. often when we are first able to detect the species in the fishery catch)”
And we know that recruitment is one of the four key population processes our stock assessment model must account for in order to accurately estimate changes in population size over time and the impacts of fishing
Growth (G)
Recruitment (R)
Natural mortality (M )
Fishing mortality (F )
Biomass
Biomass added Biomass removed

5. How is it recruitment estimated?
11/19/2018
How is it recruitment estimated?
For the tuna assessments, estimating recruitment requires:
The model being provided an equation which sets the average stock-recruitment relationship, and ensures that the model knows that at some point as adult stock declines, recruitment too will decline. MULTIFANCL models the SRR typically using the compensatory Beverton and Holt curve
The stock recruitment relationship
Spawning stock size
Total Recruitment
Declining recruitment at low stock sizes

6. How is it recruitment estimated?
11/19/2018
How is it recruitment estimated?
For the tuna assessments, estimating recruitment requires:
Data that indexes recruitment: Deviations from the SRR are determined by the strength of the size modes and the CPUE associated with those size modes.
Strong recruitment
Weak recruitment

7. 11/19/2018
The SRR and steepness
Why is it so important that the model can accurately estimate the point at which recruitment starts to decline?:
It is around this point that the stock becomes overfished…. It is no longer capable of consistently producing the recruits needed to replace the fish removed by fishing. The sustainable yield becomes reduced (it is no longer the maximum sustainable yield).
Example:
For Stock A (black line), total average recruitment starts to fall when the adult stock has declined by 70% (to 30%) of its “virgin” stock size.
For Stock B (red line) recruitment falls when the stock has declined by only 40%
i.e, the level of adult biomass below which recruitment declines differs between stocks
Stock size (% of maximum)
Total Recruitment
Indeed, even detecting the point at which overfishing starts to occur requires knowing where the overfished point is…..

8. The SRR and steepness So whats the problem?
11/19/2018
The SRR and steepness
So whats the problem?
The problem is that estimating the point (adult stock size) at which recruitment starts to decline (on average), and the rate at which it declines thereafter, is proving extremely difficult for scientists.
And uncertainty about where that point lies means uncertainty about:
What level of fishing constitutes overfishing
How low the stock can be fished before it becomes overfished
How quickly the stock might decline as fishing pressure increases
How quickly the stock might recover when fishing pressure is reduced
These are critical questions of concern to fishery managers!!
Indeed, even detecting the point at which overfishing starts to occur requires knowing where the overfished point is…..

9. 11/19/2018
The SRR and steepness
The critical parameter in a stock recruitment relationship is the steepness of the curve! This will be related to b, the stock size when recruitment is half the maximum recruitment.
Higher steepness = stock A can be depleted more before recruitment is effected, and the stock can recover more quickly from overfishing after fishing is stopped/reduced
Stock size (% of maximum)
Total Recruitment
Lower steepness = stock B can not be depleted significantly before recruitment is effected, and the stock will recover more slowly from overfishing after fishing is stopped/reduced
max b
And subsequently the estimation of MSY is also uncertain.;
Specifically it is this parameter “steepness” that is so uncertain in tuna (and other) stock assessments and results in uncertainty about stock status and management.

10. 11/19/2018
The SRR and steepness
Implications of the SRR in a real example: Estimated recruitment of bigeye tuna in the WCP-CA….
In the 50 years since industrial fishing commenced, the bigeye spawning biomass has been reduced by 85%
1. Where is the point at which we predict recruitment will start to significantly decline (ie; the fishery become overfished)?
2. How long do you think, if fishing isnt reduced, until we pass this point?
“….more commonly the number of recruits is effectively independent of adult stock size over most of the observed range of stock sizes”. (Gulland, 1983)
3. What if we got the estimate of steepness wrong?

11. The SRR and steepness Why is steepness so difficult to estimate?
11/19/2018
The SRR and steepness
Why is steepness so difficult to estimate?
Surely our size and CPUE data collected from the fishery will provide the model the signal when the adult population gets too low?
Unfortunately this is not the case……
The problem is that recruitment in tuna stocks over time is highly variable, much more so than in less productive stocks (e.g. sharks).
E.g. recruitment in a shark species
E.g. Recruitment in a tuna species
Indeed, even detecting the point at which overfishing starts to occur requires knowing where the overfished point is…..

12. The SRR and steepness
This is due to the vulnerability of tuna eggs and larvae to environmental conditions, and in particular food availability when larva hatch.
In some years, there may be abundant food for larvae and larval survival is high, where as in other years larvae may not have access to sufficient food and recruitment is subsequently lower….
The “match mismatch hypothesis” of David Cushing suggested that good recruitments will result if the adult fish can time their reproductive events to periods and areas where there is abundant food for larvae to feed upon when they first hatch.
Successful year-classes are the result of spatio-temporal “match” between first feeding larva and availability of suitable food.
Platt et al Spring algal bloom and larval [haddock] fish survival. Nature 423:

13. The SRR and steepness
The resulting variability in recruitment over time and at many different stock sizes makes it extremely difficult for a model to detect at what point the adult stock might be becoming too low to produce sufficient recruits, on average, to replace fish that are removed by fishing.
Detecting such change may mean fishing biomass substantially below Bmsy levels, an extremely high risk strategy in stocks where the adult stock is already low at that point and reductions in recruitment could become very rapid
This is partly why MSY as a target reference point is so risky (don’t know where it is without fishing past it)

14. The SRR and steepness
With no means to date by which to acquire more certain estimates of steepness, SPC scientists typically run sensitivity analyses to demonstrate to fishery managers the full impact of this uncertainty upon estimates of stock status.
It is very important that assessment scientists clearly demonstrate the implications of unknown steepness upon stock status advice…
But this is clearly less than ideal…..fisheries managers want more certainty, to reduce the risks that they might not achieve their management objectives
This is partly why MSY as a target reference point is so risky (don’t know where it is without fishing past it)

15. So what can be (and is being) done about this problem?
This is partly why MSY as a target reference point is so risky (don’t know where it is without fishing past it)

16. SPC Preliminary analysis
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’

17. SPC Preliminary analysis
Models
Ricker:
Beverton-Holt:

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

19. SPC Preliminary analysis
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:

20. SPC Preliminary analysis
Data sets
Albacore tuna
North Atlantic
North Pacific
South Pacific
Bigeye tuna
Atlantic
Indian Ocean
WCPO
Bluefin tuna
Eastern Atlantic
Skipjack
WCPO
Yellowfin tuna
Indian Ocean

21. SPC Preliminary analysis
Individual fits

22. SPC Preliminary analysis
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

23. SPC Preliminary analysis
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’

24. Preliminary results - BLUPs
SPC Preliminary analysis
Preliminary results - BLUPs

25. Preliminary results - Priors
SPC Preliminary analysis
Preliminary results - Priors

26. SPC Preliminary analysis
Next steps
Data
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

27. Initial recommendations
SPC Preliminary analysis
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