Reference Point Analysis
Western Mediterranean Hake Example
L Kell
24 September, 2021
Productivity and Reference Points
This vignette evaluates factors that affect productivity and hence reference points using Western Mediterranean hake as an example. To do this we devlop a simulation model (i.e. an Operating Model) conditioned on the latest assessment that can be used to simulate stocks under a variety of future conditions. However, unlike in Management Strategy Evaluation there is no feedback, where a Management Procedure is used to set a catch quota to update the Operating Model.
At the third Workshop on Guidelines for Management Strategy Evaluations (WGMSE3) performance statistics or summary metrics were defined as set of statistics used to evaluate the performance of Management Procedures against specified pre-agreed management objectives, and the robustness of these Management Procedures to uncertainties in resource and fishery dynamics of concern to stakeholders and managers. These are properties of the simulated system e.g. foregone catch relative to \(MSY\), or the level of a stock at which recruitment is impaired.
There are two main ways to calculate the performance statistics, namely i) using equilibrium assumptions (e.g. Sissenwine and Shepherd (1987) for age based OMs); or ii) though stochastic simulation by projecting at \(F=F_{MSY}\) or F=0 (e.g. Carruthers et al. (2016), De Moor, Butterworth, and De Oliveira (2011)). The later approach is preferable where environmental forcing or resonant cohort effects impact on productivity.
Installation
To run the the code in this vignette a number of packages need to be installed, from CRAN and the FLR website, where tutorials are also available.
Libraries
FLR
The FLR packages can be installed from www.flr-project.org
Then loaded
library(FLCore)
library(ggplotFL)
library(FLBRP)
library(FLasher)
library(FLife)
library(diags)
library(mydas)FLCandy includes various prototypes under developedment, these are being tested before migrating them to FLCore. These can be installed from GitHub
Packages
The examples make extensive use of the packages of Hadley Wickham. For example plotting is done using ggplot2 based on the Grammar of Graphics.1 Grammar is to specifies the individual building blocks and allows them to be combined to create the graphic desired2.
While ‘dplyr’ is a grammar of data manipulation, providing a consistent set of verbs that help solve the most common data manipulation challenges, while ‘plyr’ is a set of tools to split up a big data structure into homogeneous pieces, apply a function to each piece and then combine all the results back together.
library(ggplot2)
library(plyr)
library(dplyr)Historical Time series
Figure 1. Time series, from the assessment
Figure 2. Time series of weight, selectivity, maturity and M-at-age.
Productivity and Reference Points
0: 11.890259: 12.1972 -0.916291
1: 10.188522: 12.4945 -0.578722
2: 9.9148485: 12.3996 -0.600043
3: 9.8977779: 12.3416 -0.678168
4: 9.8736710: 12.3561 -0.652945
5: 9.8709823: 12.3582 -0.643693
6: 9.8705700: 12.3587 -0.639777
7: 9.8705398: 12.3576 -0.637586
8: 9.8705164: 12.3586 -0.637691
9: 9.8705161: 12.3587 -0.637802
10: 9.8705161: 12.3588 -0.637702
11: 9.8705161: 12.3587 -0.637742
12: 9.8705161: 12.3587 -0.637742Figure 3. Stock recruitment relationship, steepness unconstrained.
Figure 4. Reference points and equilibrium curves for Beverton and Holt stock recruitment relationship, \(F_{MSY}\) and \(F_{0.1}\) are shown.
Figure 5. Stock recruitment relationship by steepness.
Figure 6. Production functions.
Figure 7. Time series, with ICES PA and MSY reference points, along with MSY estimated with a Beverton and Holt stock recruitment relationship.
Projections
Status Quo
Figure 8. Reference case projections, for status quo, at \(F_{0.1}\) and \(F_{MSY}\).
Regime Shift
Figure 9. Production functions and reference points for a regime shift of 50% increase in M from 2020 onwards.
Figure 10. Regime shift of 50% increase in M from 2020 onwards, for status quo, at \(F_{0.1}\) and \(F_{MSY}\).
Trend
Figure 11. Production functions and reference points for 50% increase in M from 2020 onwards, points show \(F_{0.1}\) (dashed) and \(F_{MSY}\) (solid).
Figure 12. Regime shift of 50% increase in M from 2020 onwards, for status quo, at \(F_{0.1}\) and \(F_{MSY}\).
Shock
Figure 13. Projection at \(F_{0.1}\) for a scenario where natural mortality increased by \(50\%\) in 2020 only.
Summaries
Scenarios
Figure 14. Scenarios-at-age
Figure 15. Recovery time
Figure 16. Recovery time
Performance metrics
I suggest
- Ratio of outcomes under \(F0.1\) relative to what would have been achieved under “MSY”
- Time taken to recover after a shock
Figure 17. Potential indicators.
References
Software Versions
- R version 4.0.3 (2020-10-10)
- FLCore: 2.6.16.9004
- FLPKG:
- Compiled: Fri Sep 24 10:32:52 2021
- Git Hash: 71adb46
Acknowledgements
Carruthers, Thomas R, L.aurence T Kell, Doug DS Butterworth, Mark N Maunder, Helena F Geromont, Carl Walters, Murdoch K McAllister, et al. 2016. “Performance Review of Simple Management Procedures.” ICES J. Mar. Sci. 73 (2). Oxford University Press: 464–82.
De Moor, Carryn L, Douglas S Butterworth, and José AA De Oliveira. 2011. “Is the Management Procedure Approach Equipped to Handle Short-Lived Pelagic Species with Their Boom and Bust Dynamics? The Case of the South African Fishery for Sardine and Anchovy.” ICES Journal of Marine Science 68 (10). Oxford University Press: 2075–85.
Sissenwine, MP, and JG Shepherd. 1987. “An Alternative Perspective on Recruitment Overfishing and Biological Reference Points.” Can. J. Fish. Aquat. Sci. 44 (4). NRC Research Press: 913–18.
Wilkinson, L. 1999. The Grammar of Graphics, Springer. doi 10.1007/978-3-642-21551-3_13.↩