Expanding uncertainty scope in BEMTOOL

1. literature review and
application to case studies
Project - rete 3
Expanding uncertainty
scope in BEMTOOL
Isabella Bitetto
Maria Teresa Facchini
Maria Teresa Spedicato
Pino Lembo

2. Management Strategy Evaluation
(MSE)
Management strategy evaluation (MSE) is the process of using simulation
testing to determine how robust feedback-control management strategies are
to measurement and process error, and model uncertainty
Assessing the consequences of a range of management options and
presenting the results in a way that lays bare the tradeoffs in performance
across a range of management objectives.
T. Smith (1994)
The ability of MSE to facilitate fisheries management achieving its aims
depends on how well uncertainty is represented, and how effectively the
results of simulations are summarized and presented to the decision-makers.
André E. Punt (2014)

3. MSE Objectives
MSE is mainly used to:
• identify and evaluating suitable management
strategies for different fisheries.
MSE encompasses several source of uncertainty.
MSE provides to managers the possible trade-off of
different management strategies.

4. Few examples of MSE applications… (1)
• In south Africa to set TAC of various stock (Engraulis encrasicolus,
Merluccius paradoxus, Trachurus trachurus capensis) (Bergh and
Butterworth, 1987; De Oliveira and Butterworth, 2004);
• Since the middle of the ’80 used in the International Whaling
Commission (IWC, https://iwc.int/member-map) to manage the
catch limitations for whales (Punt and Donovan, 2007);
• Used to select managment strategies for the stock of large pelagics
(e.g.Thunnus macoyii; Tuck, 2011) (Conservation of southern
Bluefin Tuna -CCSBT, https://www.ccsbt.org/en/content/home);

5. Few examples of MSE applications… (2)
• MSE has been applied to several european fisheries to compare
several management strategies (Kell et al., 2005 a,b, 2006);
• The International Council for the Exploration of the Seas (ICES)
elaborated MSEs for 18 management plans (north-east Atlantic
stocks; STECF, 2011a;b);
• MSE has been applied to evaluate management objectives in
multispecies contexts and at ecosystem level (Sainsbury et al.,
2000; Fulton et al., 2007; Dichmont et al., 2008; 2013; Plagàny et
al., 2013).

6. Population Fleet
Operating Model
CPUE Catch
SA
& Socio-Economic
indicators
Management Process
simulation
evaluation of
stocks and fleets
management
strategies
monitoring
Management Strategy Evaluation
(MSE)

7. Population Fleet
Operating Model
CPUE Catch
SA
& Socio-Economic
indicators
Management Process
simulation
Evaluation of
stocks and fleets
Management
strategies
monitoring
Sources of uncertainty
Process
uncertainty
(Recruitment, M)
Model and
parameters
uncertainty
Measurements
and SA model
errors
Outcome
uncertainty

8. Background
During the Working Group EWG 16-20 (Bio-economic Methodology, STECF,
20171) a review has been finalised on the main characteristics of the available
bioeconomic models to evaluate management strategies with a focus on TACs.
Ten models have been analysed including BEMTOOL. This is a flexible decision
support tool, given the following features:
 several scenarios can be analysed simultaneously;
 a variety of fleets can be considered;
 technical interactions between several gears is contemplated;
 different fleet aggregations can be analysed (metier, fleet
segment, single vessels) depending on the available data.
As s decision support tool BEMTOOL uses MCDA that, in turns, allows to
take into account the stakeholder's perspective.
1STECF, 2017. Bio-Economic Methodology (EWG-17-05); Publications Office of the European Union,
Luxembourg; EUR 28359 EN; doi:10.2760/759034

9. Objectives of WP2 in RETE3
Objectives of WP2 are to make BEMTOOL fully in line with
MSE, exploiting the model flexibility to incorporate
uncertainty at different levels/components. This will
further enable the evaluation of different management
measures given the implementation of:
• process error;
• model error.

10. Process uncertainty
This kind of uncertainty is linked to the biological processes.
To incorporate this kind of uncertainty in the stock-recruitment
relationships implemented in BEMTOOL, three approcches have been
tested:
1. a grid of parameters extracted from a uniform distribution;
2. a grid of parameters derived by the EqSim approach;
3. a grid of parameters extracted from a normal distribution.

11. Stock-recruitment relationships
implemented in BEMTOOL
• Beverton-Holt;
• Ricker;
• Sheperd;
• Hockey stick;
• Quadratic hockey stick.
The model foresees the possibility of simulating stock recruitment
relationships which are even modulated by an additional
environmental variable (to be inputed with the S-R parameters).
The hockey stick S-R has been used to test the uncertainty
approaches.

12. Stock-Recruitment
hockey-stick stock-recruitment (or
segmented regression)
Recruits(t+1) = min (a*SSB(t), b)
the parameters estimated in the
deterministic S-R are:
a = 1200 (CV=0.12)
b = 400 tons (CV=0.05)
The assumption is that the confidence interval is more narrow in the
ascending tract of the curve, where observations are more numerous,
and wider in the horizontal tract (limited or null number of observations).

13. Approach 1
(uniform distribution)
350
360
370
380
390
400
410
420
430
440
450
700 900 1100 1300 1500
b
a
1. using the deterministic parameters of the S-R and the CV
the CI has been estimated;
2. this interval has been subdivided in equal segments to
create a regular grid of 1000 pairs of parameters (a,b);

14. Approach 2 (Eqsim)
Eqsim (stochastic equilibrium reference point
software, https://github.com/ices-tools-prod/
msy, ICES, 2015 e Minto et al. 2014) estimates
reference points (e.g. MSY) on the basis of
stochastic projections of a population in
equilibrium.
Productivity variables (natural mortality,
individual weight-at-age, maturity at age) are
resampled using the last years of the
assessments.
Eqsim estimates S-R relationships, resampling
the pairs recruits-spawners from the
assessment and estimating 1000 times the S-R
parameters.
The 1000 pairs of the S-R parameters have been estimated by Eqsim, using the
same inputs (assessment results) as in the approach 1.

15. Approach 3
(Kell et al., 2005)
1000 pairs of parameters of the S-R relationships have been extracted
from 2 normal distributions with mean sets equal to the deterministic
values of the S-R parameters and standard deviation given by CV*mean
(CV defined a priori).

16. Comparison of the 3 methods
• the S-R relationships from the approach1 are regular and equally
distributed;
• Eqsim realizations (approach 2), are instead more concentrated;
• approach 3 gives a set of curves similar to approach 1 with some
outliers (tails of the distributions of the parameters a e b.)

17. Tests of the three approches
1. two scenarios:
• status quo;
• increase selectivity
(alternatively reduction of the effort in fishing days to the achievement of the
reference point)
BEMTOOL makes 1000 runs, one for each pairs of parameters, in
each scenario. From the results of the 1000 runs, median values
and percentiles of the main indicators (e.g. SSB, landings, discards,
economic variables) are estimated ;
For each scenario two hypotheses for price are set:
i. price dependent by the landing through an elasticity coefficient;
ii. price dependent by the landing volume and by the mean weight
of the landed individuals through elasticity coefficients.

18. Hypotheses of the price functions







 −
+=
−
−
−
1,,
1,,,,
,,1,,,, 1
tfs
tfstfs
landingfstfstfs
L
LL
pp ε
fsf
tfstfslasttfstfs Lpp ,,1
,,,,,,,,
εγ
ω==
where:
ps,f,t-1 is the price of the stock s, of the fleet f at time t-1;
Ls,f,t-1 is the landing of the stock s, of the fleet f at time t-1;
is the elasticity coefficient between price and landings (=-0,2);
where:
ps,f,last is the price of the stock s, of the fleet f at the current time (=last);
Ls,f,t is the landing of the stock s, of the fleet f at time t;
is the average weight of the individual fish in the landing;
is the elasticity coefficient between price and landing;
is the elasticity coefficient between price and average individual weight (=1.1)
f
tfs
,1
,,
γ
ω
ε
ε
f,1γ

19. Case study 1
Anchovy GSA17 and 18 (GFCM WKMSE 2016)
Scenarios:
• Status quo
• effort reduction of 45% in fishing
days in order to achieve E=0.4
Price dependent by landing volume

20. Results (SSB)
Status quo: comparison of the
three approaches on uncertainty
effort reduction: comparison of the
three approaches on uncertainty

21. Results (landing)
effort reduction: comparison of the
three approaches on uncertainty
Status quo: comparison of the
three approaches on uncertainty

22. Revenues
Status quo: comparison of the
three approaches on uncertainty
effort reduction: comparison of the
three approaches on uncertainty

23. Case study 2
Stock of deep-water rose shrimp P. longirostris in the
GSA 19 (Russo, Bitetto et al., 2017). This stock is
exploited by 5 trawl fleets in 10 fishing grounds (FG):
FG Origin of vessels fishing in the FG metier LOA
A Otranto – Mola di Bari - Gallipoli OTB_DES 12-18; 18-24
B-C-D
Gallipoli-Taranto-Corigliano – Cariati
- Cirò
OTB_MDD 12-18; 18-24
E-G-H Crotone-Roccella- Catania OTB_MDD 12-18; 18-24
F Le Castelle – Catanzaro Lido OTB_DES 12-18
I-L Catania – Capo Passero - Siracusa OTB_DES 12-18; 18-24

24. Results (SSB) scenarios' comparison in the three approaches
comparison of the three
approaches in two scenarios:
status quo (left graph) and
increase selectivity (right graph)

25. Revenues in the Status quo
comparison of the three uncertainty approaches in the staus quo scenario without (left
graph) and with (right graph) elasticity between price and mean individual weigth

26. Revenues in the scenario with increased selectivity
The three approaches of uncertainty of the S-R are compared considering the
two hypotheses of price. The additional elasticity between mean individual
weight and price (right graph) results in higher revenues compared to the
hypothesis of elasticity between price and landing volume only.

27. Pros and cons of the three methods analysed to
introduce uncertainty in the S-R relationship
Approach 2 (Eqsim) generally results in a narrower confidence
interval, more close to the observed values; this method could be
more suitable in situations with time series long enough and with
contrasted values;
Approach 3 (extraction from a normal distribution) could be useful
when the time series is shorter but there are hypotheses on the
error distribution around the S-R parameters;
Approach1 (regular grid or uniform distribution) could be applied
when a long and contrasted time series is not available and there
are not hypotheses on the distribution of the error around the
parameters of the S-R .

28. Further sources of
uncertainty in BEMTOOL
Process error:
Growth parameters;
Natural Mortality;
Model error:
Maturity;
Selectivity.

29. Uncertainty on the growth - process error
BEMTOOL accounts for the uncertainty on growth using a probability
distribution with parameters µ and σ associated to L∞ or to k.
Once 1000 realizations of either one or the other of the two growth
parameters have been made, 1000 realizations of the other parameter are
extracted through an optimization process based on the lengths and the
deterministic VBGF (R optim). The parameter t0 is fixed.

30. Uncertainty on the growth - process error
probability density function of 1000 realizations of L∞ afroma normal pdf
with mean 100 and standard deviation 10 cm.
empirical pdf of the 1000 k estimates obtained
through the optimization process

31. Uncertainty on the natural mortality – process error
L’incertezza incorporata nei
parametri di crescita, e in
particolare quella su k, si
propaga anche sulla mortalità
naturale attraverso
l’equazione di
Chen&Watanabe (1989) .
100 realizations
Chen and Watanabe model of M

32. Uncertainty on the maturity - model error
Using a pdf and the
parameters of the maturity
function, the model
propagates the uncertainty
on the population and on
the SSB through the S-R
relationship.

33. Uncertainty on the selectivity - model error
Using a pdf and the
parameters of the
selectivity functions, the
model propagates the
uncertainty on the
population and on the
catches.

34. Conclusions
In the Rete 3 project we have expanded the scope of
addressing uncertainty sources in BEMTOOL, considering
both process and model error.
BEMTOOL should thus result more robust when it forecasts
the impact of different management alternatives, giving
managers a more complete feedback for taking decision.