MULTIFAN-CL implementation of deterministic and stochastic projections

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

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

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

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

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

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

Example of deterministic projection command: mfclo32 bet.frq proj.par tttt -switch 2 1 1 1 -999 55 0 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

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)

Flow diagram of stochastic projections in simulations Simulation start HISTORICAL Model run 1952-2008 Stochasticity: recruitments 2009-2018 Numbers at age in first projection year Effort deviates 2009-2018 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. 1952 – 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 2009-2018 Store Projection biomass Simulation finish Calculate risk Bproj < BLRP

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

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)

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

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

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

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.

Projections results Fig. 2

Bigeye tuna results Table 1

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