1. MULTIFAN-CL implementation of deterministic and stochastic projections

2. Overview Projection concept
Implementation of a deterministic projection
Stochastic projection algorithm
Examples of stochasticity - biomass
Implementation of stochastic projections for evaluating BLRPs

3. Projection concept
Assessment model provides estimates of current stock status
Of interest to managers is: “what if?”, “what catch?”
Estimation period
Projection period ?
Parameters
applied
Parameters estimated

4. Implementation of a deterministic projection
Inputs:
Assessment model parameter estimates
Assume these remain constant over the projection period
Extend certain parameter time series over a projection period
Extend fisheries data over a projection period
Run model

5. Flow diagram of creating inputs for MFCL deterministic projection algorithm
User input
Species
MPD files
Projection years
Baseline years (status quo)
Special case fisheries
7. Deterministic projection
Single evaluation with proj.par and projn frq
4. Construct projection frq
Create additional data
Confirm columns 7 - 9
Write new frq
2. Fishery data
Get predicted effort data for incomplete fisheries
Check for missing data
Check for penalty wts
ID/PH fisheries insert 1
Store original MPD frq
Write new MPD frq
8. Store baseline projn frq
Copy to storage
5. Makepar for new 00.par
New projn frq
Produce 00.par
9. Modify projn frq and re-run projn
Call mak.scld.frq2 to scale fishery data in projection period (scen.frq)
Copy files
Single evaluation with proj.par and scen.frq
6. Construct proj.par
Input new MPD par
Input 00.par
Merge sections
Add parameters for projection period
Write proj.par
3. Re-estimate MPD
Run 200 evaluations
Obtain new “q”
Confirm new MPD

6. List of parameter time series extended
Projection *.par file:
Format proj.par according to dimensions of 00.par
Extend parameters:
predicted future recruitments
reporting rate deviates
fm_level_devs
regional recruitment variation
effort deviation coefficients
catchability deviation coefficients
selectivity deviation coefficients
cohort specific growth deviations
grouped_catch_dev_coffs

7. Fisheries data extended in *.frq
Projection *.frq file:
Insert first projection year and month in data flags
Extend fisheries
catch and effort
Assumed catch or
effort for projection
management strategy
Missing catch or
effort data: insert -1

8. Example of deterministic projection
command:
mfclo32 bet.frq proj.par tttt -switch
MFCL command accesses the projection versions of the *.frq and *.par files, and runs the model for a single evaluation
Examples of deterministic projection results:
Illustration of projected biomass for each region
Total biomass over all regions under a range of management strategies

9. Stochastic projection algorithm
A series of “deterministic” projection iterations with stochastic variation in each
Sources of variation:
Recruitment (random resampling with replacement)
Numbers at age in the 1st year of the projection (parametric)
Effort deviates (parametric)
Constants: fisheries data, other parameters
Variance calculations from model estimates over the analysis period – used to generate stochastic data (parametrically)

10. Flow diagram of stochastic projections in simulations
Simulation start
HISTORICAL
Model run
Stochasticity:
recruitments
Numbers at age in first projection year
Effort deviates
Specify
Projection fishery catch or effort
200
simulations
This flow diagram shows how a projection biomass was calculated.
- First we run the population model over the calculation period used in the assessment, e.g – 2008
Second we generate a set of stochastic (i.e. random) recruitments for each time period in the future used for the projections. These are sampled from the historical recruitments.
Thirdly we run the model with the future recruitments over the projection period and store the future biomass estimates.
This repeated over a large number of simulations (in our case 200), and from this set of simulation estimates of future biomass, a distribution is calculated. By examining the left-hand tail of the distribution, one calculates the risk of biomass being below the BLRP.
But how do we then design a strategy that achieves the target level of risk associated with the BLRP? …..
PROJECTION
Model run
Store
Projection biomass
Simulation finish
Calculate risk Bproj < BLRP

11. Stochastic recruitments
Total biomass – stochastic projections - example for 20 simulation projections
Stochastic recruitments + eff.devs

12. Implementation of stochastic projections for evaluating BLRPs
Previous work…
A FRAMEWORK TO EVALUATE THE POTENTIAL IMPACTS OF LIMIT REFERENCE POINTS, INCLUDING MULTI-SPECIES CONSIDERATIONS (SC6-MI-WP-01)

13. Overview Work aimed to address the request from SC5:
3. Evaluation of the consequences of adopting particular LRPs based on stochastic projections using the stock assessment models.
No candidate LRPs forthcoming so we have focused on the methodological framework

14. Reference points and risk levels used
½ SBMSY and 0.2SB0
With risks of 5% and 10%
Find ‘management strategies’ that achieve these four combinations of reference point and risk using run 14 from the 2009 assessment

15. Algorithm search for future effort satisfying BLRP
Effort scalar
Scaled future effort
Simply we embed the entire simulation procedure within a search for a scalar of future effort.
The process is:
Starting with the status quo effort level we do the simulations and calculate the risk relative to the BLRP. (i.e. using a scalar = 1)
From the simulations the risk level is calculated relative to the BLRP target risk.
If it is higher or lower the effort scalar is applied to scale the future effort used in the projections and the simulations are run again.
This process is repeated over a number of iterations using a Hillclimb algorithm to solve for the required scalar that achieves the BLRP risk level.
This then provides the means for designing management strategies that achieve a desired BLRP specified level of risk. NO
Required future effort for BLRP
Test risk = BLRP % risk
YES

16. This shows a hypothetical distribution for population biomass at the end of a projection period, say generated from a large number of simulations. One can determine on the left hand tail what level the biomass is below which 5% of the distribution occurs. This translates directly to a 5% probability or risk that the biomass will be below this level. The aim of management might be to maintain biomass so that there is less than or equal to a 5% probability that the biomass is below the BLRP. One would then seek to design a management strategy that would achieve this, i.e. to shift the distribution to the left or to the right to fit, i.e., to target the centre of the distribution so that the left had tail is positioned to coincide the 5%ile at the BLRP as shown. The next slides explain the approach taken in this study to achieve this.

17. Projections results
Fig. 2

18. Bigeye tuna results
Table 1

19. Summary – stochastic projections
Framework is practical, not unduly computationally intensive, and is consistent with approaches used to estimate risk and exceeding reference points (e.g. Kobe-II strategy matrix).
We refer to this framework as a Yield Management Catch Analysis
Can be used for both:
Estimating risk associated with a given management strategy
In developing management strategies