WKLife
WKLife
ToR
- Establish relationships between life-histories and biological reference points in order to develop robust proxies for \(F_{MSY}\) and \(F_{lim}\).
Long-term goals
- Develop robust catch rules
- Condition Operating Models on
- fishing history, depletion levels, selectivity assumptions, natural mortality.
- Diagnostics
- Consider nature of Time-series
mydas
- Develop Proxy \(MSY\) Reference Points across the spectrum of data-limited stocks.
- Diagnostics for screening reference points, assessment methods, HCRs and MPs
- Management Strategy Evaluation to develop plans to manage risk given uncertainty
Screening Indicators
Indicators
- \(L_{max5\%}\) mean length of largest 5%
- \(L_{25\%}\) \(25^{th}\) percentile of length distribution
- \(L_{c}\) Length at \(50\%\) of modal abundance
- \(L_{mean}\) Mean length of individuals \(> L\)
- \(L_{bar}\) Mean length
- \(L_{max_{y}}\) Length class with maximum biomass in catch
- \(L_{95\%}\) \(95^{th}\) percentile
- \(P_{mega}\) Proportion of individuals above \(L_{opt} + 10\%\)
Reference points
- \(L_{opt} = L_{\infty}\frac{3}{3+\frac{M}{K}}\), assuming \(M/K = 1.5\) gives \(\frac{2}{3}L_{\infty}\)
- \(L_{F=M} = 0.75l_c+0.25l_{\infty}\)
- \(f^{'} = \bar{L}_{y-1}/L_{mat}\)
- \(f^{''} = min(1, \bar{L}_{y-1}/L_{mat})\)
- \(f^{'''} = min(1, \bar{L}_{y-1}(1-d)/L_{mat})\) for d > 0
Robustness
Simulate stocks, different values of \(k\), \(h\), … and fuctional forms and compare proxies to \(MSY\) reference points
Life History Parameters
Life history parameters by species, species ordered by \(k\)
Simulations
Simulated time series
Length distributions
Sampled length distributions for different periods.
Receiver Operating Characteristic
Receiver Operating Characteristic curves for recovery period, the points correpond to the ICES reference level (red) and the best descriminate threshold (black), ordered by k and percentile.
Area under the curve
Area under ROC curve, a good length based indicator should have a high area close to 1.
Impact of uncertainty
Euclidean distance from TPR=1 and FPR=0.
Emprical Control Rules
Used Machine Learning
- Perform random search then use
- Support vector regression to model relationship between performance measures and control parameters
- Genetic algorithms to find pareto Frontiers
Trends
Empirical HCR catches are increased when the trend in an index is positive, and decreased if the trend is negative
\[TAC^1_{y+1}=TAC_y\times \left\{\begin{array}{rcl} {1-k_1|\lambda|^{\gamma}} & \mbox{for} & \lambda<0\\[0.35cm] {1+k_2\lambda} & \mbox{for} & \lambda\geq 0 \end{array}\right. \]
where \(\lambda\) is the slope in the regression of \(\ln I_y\) for the most recent \(n\) years, k1 and k2 are parameters and \(\gamma\) actions asymmetry so that decreases in the index do not result in the same relative change as as an increase.
Pareto Frontiers
Time series for an example simulation.
Strict condition \(P(B>B_{lim}\)) > 0.95
Simulations for random combinations of control parameters (k1 and k2), colours showing probability of Blim > 95%.
Pareto Optimal Solutions
A Pareto plot for objectives corresponding to maximising yield and minimising average annual variation in yield (AAV), non-optimal solutions and optimal solutions that lie along the Pareto front are indicated.
Pareto Frontiers
A Pareto plot for objectives corresponding to maximising yield and minimising average annual variation in yield (AAV), non-optimal solutions and optimal solutions that lie along the Pareto front are indicated.
Calibration Regressions
Calibration regressions identifing the 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
Summary statistics, for the MSEs run for the a single set of control parameters, k1=0.6 and k2=0.6.
Elasticity
Simulations
Kobe phase plot with trajectory.
Biomass
Elasticity of \(SSB/SSB_{MSY}\) as a function of fishing mortality.
Harvest rate
Elasticity of \(F/F_{MSY}\) as a function of fishing mortality.