WKGMSE3

ToR b) Develop more efficient ways of conducting searches over a grid to the required level of precision be investigated.

  • This is needed because of the high-performance computing requirements for full MSEs.
  • This work could include investigating statistical properties that relate sample size to required precision, GAMs to interpolate over an incomplete grid, etc.

WKLife

Workshop on the Development of Quantitative Assessment Methodologies based on LIFE-history traits, exploitation characteristics, and other relevant parameters for data-limited stocks

MyDas

Aim is to develop Proxy \(MSY\) Reference Points across the spectrum of data-limited stocks; this required

  • Diagnostics for screening
    • Assessment methods
    • Indicators
    • Reference points
    • HCRs and MPs
  • Management Strategy Evaluation to develop plans to manage risk, where
    • Risk is an uncertainty that matters and what matters are management objectives.

Emprical Control Rules

Already used to provide advice for ICES Category 3 stocks, e.g. those for which survey-based assessments can provide an indication of trends.

This includes indicators of stock size or exploitation rate such, e.g.

  • survey indices, CPUE, mean length, …

Rule

Catches are increased when the trend is going up, and decreased when going down

\[TAC^1_{y+1}=TAC_y\times \left\{\begin{array}{rcl} {1+k_1\lambda} & \mbox{for} & \lambda<0\\[0.35cm] {1+k_2\lambda} & \mbox{for} & \lambda\geq 0 \end{array}\right. \]

\(\lambda\) is the slope from the regression of recent values of an index \(\ln I_y\) on year (\(y\))

\(k_1\) and \(k_2\) are gain terms and action asymmetry, since increasing catch in error is not the same as incorrect reduction. In the former if a stock becomes overexploited it may require a long-term closure, while in the later catches are banked and may be taken once the error is realised.

Management Objectives

  • Risk of falling below \(B_{lim}\)
  • Maximising long-term yield
  • Reducing inter-annual variability in catch or effort

\(MSY\)

No need to explicitly consider \(B_{MSY}\) or \(F_{MSY}\), since if the stock is sustainable and yield is maximised then by definition \(MSY\) objectives are met.

Operating Model

Pollack based on life history theory

Time series for an example simulation.

Time series for an example simulation.

There is no single utility function as different stakeholders weight objectives differently.

  • Use Genetic algorithm to find Pareto Frontiers to explore trade-offs between multiple objectives.

Machine Learning

Use Random Search to explore the impact of \(k_1\) and \(k_2\) on management objectives, i.e.

Use Support vector regression to model the relationship between control parameters and performance measures. Makes no assumption about distributions of variables, and no need for transformations.

Strict condition \(P(B>B_{lim}\)) > 0.95

If the stock is not sustainable then the MP is not acceptable

Simulations for random combinations of control parameters (k1 and k2), colours showing if probability $B_{lim}$ > 95%.

Simulations for random combinations of control parameters (k1 and k2), colours showing if probability \(B_{lim}\) > 95%.

Pareto Optimal Solutions

Once the stock has been shown to be sustainable, let stake and asset holders agree amongst themselves who can take what when.

Pareto plot for yield and average annual variation in yield (AAV)

Pareto plot for yield and average annual variation in yield (AAV)

Optimal solutions lie along the Pareto front, you can not improve one objective without trading off others. Non-optimal solutions can always be improved.

No need to agree utilty of stakeholders before running MSE, as these can always be elicited later.

Scenarios

Observation Error Model

  • Variability of index 10%, 20%, 30%

Control Options

  • Length of series used in estimation of trend, i.e. 3, 5, … years.

Pareto Frontiers

How to improve performance, i.e.

  • Better data or
  • Change rule?
Pareto plot for maximising yield and average annual variation in yield (AAV)

Pareto plot for maximising yield and average annual variation in yield (AAV)

Calibration Regressions

Values of k1 and k2 to achieve a given Pareto optimal solution; vertical lines correspond to $80% MSY$, AAV value derive from the Pareto optimum.

Values of k1 and k2 to achieve a given Pareto optimal solution; vertical lines correspond to \(80% MSY\), AAV value derive from the Pareto optimum.

MSE

Conduct MSE once objectives are agreed.

Summary statistics, for the MSEs run for the a single set of control parameters, k1=0.6 and k2=0.6.

Summary statistics, for the MSEs run for the a single set of control parameters, k1=0.6 and k2=0.6.

Summary

  • Although only 1 OM scenario was considered, multiple OMs could have been conditioned and SVR used to model the relationship between control variables and summary statistics.
  • SVR could be conducted on a scenario by scenario basis, or if probabilities can be assigned to OMs then either a weighted random search or a weighted SVR analysis conducted.
  • The approach allows a Value-of-Infomation and Value-of-Control analysis to be performed, i.e. to show how a reduction in uncertainty can reduce risk of management objectives not being met.

Conclusions

a) Develop guidelines for when and how reference points should be extracted from an MSE when one is conducted.

  • There are no explicit reference points developed in the MP, \(k_1\) and \(k_2\) are tuned, i.e. varied until the parameters values that best meet management objectives are found.
  • The same procedure can be used for model based HCRs, where a biomass dynamic assessment model provides estimates of \(B_{trigger}\) based on exploitable biomass and \(F_{MSY}\) based on harvest rate. These may be related to, but are not the same as the reference points, based on \(SSB\) and instantaneous mortality used in the OM.

b) Develop guidelines for how to treat the results of alternative operating models. Currently, these have been used as robustness tests for “optimised” management strategies.

  • How to propose and agree?
  • How to reject and weight probabilities?
    • Conditioning is The process of fitting an Operating Model (OM) of the resource dynamics to the available data on the basis of some statistical criterion, such as a Maximum Likelihood. The aim of conditioning is to select those OMs consistent with the data and reject OMs that do not fit these data satisfactorily and, as such, are considered implausible.
    • Plausibility is the likelihood of a scenario considered in simulation trials representing reality, relative to other scenarios also under consideration. Plausibility may be estimated formally based on some statistical approach, or specified based on expert judgement, and can be used to weight performance statistics when integrating over results for different scenarios (OMs).
  • Evalute robustness? i.e. objectives must be met for all OM scenarios

d) Develop more efficient ways of conducting searches over a grid to the required level of precision be investigated. This is needed because of the high-performance computing requirements for full MSEs. This work could include investigating statistical properties that relate sample size to required precision, GAMs to interpolate over an incomplete grid, etc.

  • Use Randon search and then GA & SVR to model relationship between control parameters and management objectives
  • Make elicitation of objectives as the main objective of MSE.

e) Compare the short-cut and full MSE approaches, providing guidelines for use of the former as an approximation for the latter, if appropriate. Consideration should be given to MSE with alternative operating models (i.e. operating models not solely based on the currently-used assessment).

Use Randon search and then GA & SVR to evaluate relationship between control parameters and management objectives