Mathematics of BioEconomics MABIES Quantitative tools for the sustainable recovery of the hake Merluccius Gayi Gayi in the Region o f Valparaiso Chile Project started at August 2011 ID: 302002
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Slide1
February 6, 2013 - Institut Henri Poincaré – Paris - France
Mathematics of Bio-Economics (MABIES)
Quantitative tools for the
sustainable
recovery
of the hake (Merluccius Gayi Gayi) in the Regionof Valparaiso, ChileSlide2
Project started at
August, 2011
Duration
1.5 year
Current Stage
Online tool on final development stage
Project website
www.recuperemoslamerluza.cl
Financial support
Regional Government (GoRe) Valparaiso; Program for the Innovation & Competitiveness (FIC)
This project has been carried by a multidisciplinary team and has been leading by
Department of Mathematics, Universidad Técnica Federico Santa María, Chile.Slide3
Research
Team
Multidisciplinary Group
Marine Biologists
Engineers
Applied Mathematicians
Expert on social behavior
Journalist
PEDRO
GAJARDO
HÉCTOR
RAMÍREZ
ALEJANDRO
ZULETA
DARÍO
RIVAS
RENZO
TASCHERI
MAXIMILIANO
OLIVARES
RESEARCHER ON
MATHEMATICAL
MODELLING
PROJECT DIRECTOR
RESEARCHER ON
FISHERIES
MANAGEMENT
RESEARCHER ON
FISHERIES STOCK
ASSESMENT
MARINE
BIOLOGIST
MATHEMATICAL
ENGINEERING
STUDENT
COLLABORATORS
GILDA MEDINA
|
JOURNALIST
HÉCTOR TRUJILLO
|
SOFTSYSTEMS ANALYSIS GROUP (VENEZUELA)
ANGGELO URSO
|
COMPUTER ENGINEERING
RESEARCHER ON
MATHEMATICAL
MODELLING
ADJOINT DIRECTORSlide4
Oldest and most important demersal fishery in Chile
Main fishery resource of the Region
of
Valparaiso
Hake
FisherySlide5
In the last decade, the South Pacific Hake's (
Merluccius Gayi Gayi
) fishery has been
very damaged
SOME DISCUSSED EXPLAINATIONS
OVEREXPLOITATION
APPARITION OF
NEW PREDATORS
GIANT
SQUID
Hake
FisherySlide6
This situation has led to a reduction of landings and, consequently, to a reduction of the artisan fleet in the Region of Valparaiso (Chile)
Landings (tonnes) of hake. The red line shows the annual global catch quota established and approved by the CNP since 1992.
Source: Technical Report (R.Pesq.) N°117/2011
Hake
FisherySlide7
The aim of this project is to provide quantitative tools to propose recovery strategies for this fisherySlide8
StakeholdersSlide9
Stakeholders
Yields
Landings / catchesSlide10
Stakeholders
Yields
Prevention
Landings / catches
SSB
Spawning
Stock BiomassSlide11
Stakeholders
Yields
Landings / catches
Prevention
SSB
Spawning
Stock Biomass
Social
Requirement
Level of yields required by the local communitySlide12
Landings / catches
SSB
Spawning
Stock Biomass
Stakeholders
Level of yields required by the local community
Yields
Social
Requirement
PreventionSlide13
Landings / catches
SSB
Spawning
Stock Biomass
Stakeholders
Yields
Prevention
Social
Requirement
Recovery Plan
Proposal
Level of yields required by the local communitySlide14
Landings / catches
SSB
Spawning
Stock Biomass
Stakeholders
Yields
Prevention
BIOLOGICAL INDICATORS
Spawning Stock Biomass
Total Biomass
Social
Requirement
Recovery Plan
Proposal
Level of yields required by the local communitySlide15
Landings / catches
SSB
Spawning
Stock Biomass
Stakeholders
Yields
Prevention
BIOLOGICAL INDICATORS
Spawning Stock Biomass
Total Biomass
ECONOMICAL INDICATORS
Landings
Economical return of the fleets
Social
Requirement
Recovery Plan
Proposal
Level of yields required by the local communitySlide16
Landings / catches
SSB
Spawning
Stock Biomass
Stakeholders
Yields
Prevention
BIOLOGICAL INDICATORS
Spawning Stock Biomass
Total Biomass
ECONOMICAL INDICATORS
Landings
Economical return of the fleets
The plan will be
optimal
in some predefined sense
Social
Requirement
Recovery Plan
Proposal
Level of yields required by the local communitySlide17
Stakeholders
Meetings with stakeholdersSlide18
Meetings with stakeholders
Stakeholders
To introduce
the project
To obtain feedbackSlide19
Meetings with stakeholders
Stakeholders
To introduce
the project
To obtain feedback
Bottom-up relation
with the different actors involved in the fishery managementSlide20
Stakeholders
3 Stages
Visiting local fishing bays
Stage I
Interviews with stakeholders
in the
Region of Valparaiso
Stage II
“Identifying the
main problems
for the recovery of hake”
Stage III
WORKSHOPSlide21
Stakeholders
3 Stages
Visiting local fishing bays
Stage I
Interviews with stakeholders in the
Region of Valparaiso
Stage II
“Identifying the
main problems
for the recovery of hake”
Stage III
WORKSHOPSlide22
Stakeholders
3 Stages
Visiting local fishing bays
Stage I
Interviews with stakeholders in the
Region of Valparaiso
Stage II
“Identifying the
main problems
for the recovery of hake”
Stage III
WORKSHOP
Eduardo Quiroz
“Portales”
Miguel Ángel Hernández
“Puertecito”
Gabriel Valenzuela
“El Membrillo”
Valparaíso
Valparaíso
San AntonioSlide23
Stakeholders
3 Stages
Visiting local fishing bays
Stage I
Interviews with stakeholders in the
Region of Valparaiso
Stage II
“Identifying the
main problems
for the recovery of hake”
Stage III
WORKSHOPSlide24
Workshop
“Identifying the
main problems
for the recovery of hake”
Some key macroproblems
The State, the Academy, Civil Society and Business (Industrial-Artisan Fisheries) operating as bubbles
From interviews and email consults to different stakeholders (in the Region of Valparaiso), were identified 20
‘macroproblems’
There is no a joint sociopolitical vision for the
exploitation of the hake fisherySlide25
THEORY
WORKSHOPS &
STAKEHOLDERS
RESEARCH
TEAM
FISHERIES
STOCK
ASSESSMENT
WEBWARE
WEB APPLICATION
OPEN ACCESS
Technological TransferSlide26
WEBWARE
WEB APPLICATION
OPEN ACCESS
THEORY
WORKSHOPS &
STAKEHOLDERS
RESEARCH
TEAM
FISHERIES
STOCK
ASSESSMENT
Technological TransferSlide27
Technological Transfer
THEORY
WORKSHOPS &
STAKEHOLDERS
RESEARCH
TEAM
FISHERIES
STOCK
ASSESSMENT
WEBWARE
WEB APPLICATION
OPEN ACCESSSlide28
Theory
BASIC IDEASSlide29
Theory
BASIC IDEAS
FISHERIES DATA
ESTIMATION
MEAN
WEIGHT
+ OTHERS
ABUNDANCE
ESTIMATIONSlide30
Theory
BASIC IDEAS
FISHERIES DATA
ESTIMATION
MEAN
WEIGHT
+ OTHERS
ABUNDANCE
ESTIMATION
N
ABUNDANCE VECTOR
OR
STATESlide31
Theory
BASIC IDEAS
INITIAL STATE
N
0Slide32
Theory
BASIC IDEAS
Y
t
N
0
Yields | Landings | Catches
[ktonnes]
[years]
FROM
t
0
Yields from some strategy
…
INITIAL STATE
N
0Slide33
Theory
BASIC IDEAS
Y
t
N
0
[ktonnes]
[years]
FROM
t
0
…
y
min
INITIAL STATE
N
0
We focus on minimal sustainable value for yield
Yields | Landings | Catches
y
minSlide34
Theory
BASIC IDEAS
N
0
FROM
INITIAL STATE
N
0
We seek strategies which ensures instead of
…
Y
t
y
min
[ktonnes]
[years]
N
0
FROM
…
Y
t
y
min
[ktonnes]
[years]
y
min
as minimal
sustainable
value for yield
y
min
By modifying the exploitation strategy
y
minSlide35
Theory
BASIC IDEAS
INITIAL STATE
N
0
y
min
y
min
?
What is the maximum possible value for y
min
?
…
Y
t
y
min
[ktonnes]
[years]
y
min
Mm
y
min
N
0
FROM
Yields | Landings | CatchesSlide36
Theory
BASIC IDEAS
INITIAL STATE
N
0
N
0
FROM
Mm
We can use this value to propose a recovery plan
Mm
y
min
Yields | Landings | CatchesSlide37
Theory
BASIC IDEAS
INITIAL STATE
N
0
N
0
FROM
Mm
Recovery
Problem
Mm
Maximum possible value for y
minSlide38
Theory
BASIC IDEAS
INITIAL STATE
N
0
N
0
FROM
Mm
Mm
Maximum possible value for y
min
REQ
Recovery
Problem
REQ
Social required level for yieldSlide39
Theory
BASIC IDEAS
INITIAL STATE
N
0
N
0
FROM
Mm
Mm
Maximum possible value for y
min
REQ
Social required level for yield
REQ
Recovery
Problem
What strategy can be used to pass from N
0
to a “healthy” fishery N(T)?
N
0
N(T)Slide40
Theory
BASIC IDEAS
INITIAL STATE
N
0
N(T)
FROM
Mm
REQ
Recovery
Problem
Mm
Maximum possible value for y
min
REQ
Social required level for yield
N
0
N(T)
What strategy can be used to pass from N
0
to a “healthy” fishery N(T)?Slide41
Theory
BASIC IDEAS
INITIAL STATE
N
0
N(T)
FROM
Mm
Mm
Maximum possible value for y
min
REQ
Social required level for yield
REQ
Recovery
Problem
What strategy can be used to pass from N
0
to a “healthy” fishery N(T)?
N
0
N(T)Slide42
Theory
BASIC IDEAS
Mm
Maximum possible value for y
min
REQ
Social required level for yield
RECOVERY
PLAN
REQ
REQ
Mm
Mm
T years
Constant Total Allowable
Catches (Yields)
N(T)
N
0
Recovery
Problem
What strategy can be used to pass from N
0
to a “healthy” fishery N(T)?
N
0
N(T)Slide43
Mm
Maximum possible value for ymin
REQ Social required level for yield SSB Mínimum value for SSB according Mm SSB
min Required SSB prevention level
Theory
BASIC IDEAS
REQ
REQ
Mm
Mm
N(T)
N
0
Recovery
Problem
SSB
SSB
RECOVERY
PLAN
T years
Constant TAC (Yields)
SSB
min
SSB
min
What strategy can be used to pass from N
0
to a “healthy” fishery N(T)?
N
0
N(T)Slide44
Theory
BASIC IDEAS
RECOVERY
PLAN
REQ
REQ
Mm
Mm
T years
Constant TAC (Yields)
N(T)
N
0
Recovery
Problem
SSB
SSB
TRADEOFF:
COST= REQ-TAC
OPTIMIZATION PROBLEM:
WHAT IS THE RECOVERY
PLAN WITH MINIMAL COST?
SSB
min
SSB
min
Mm
Maximum possible value for y
min
REQ
Social required level for yield
SSB Mínimum value for SSB according Mm
SSB
min
Required SSB prevention level
What strategy can be used to pass from N
0
to a “healthy” fishery N(T)?
N
0
N(T)
[ Dynamics and Optimization Problem]Slide45
Technological Transfer
THEORY
WORKSHOPS &
STAKEHOLDERS
RESEARCH
TEAM
FISHERIES
STOCK
ASSESSMENT
WEBWARE
WEB APPLICATION
OPEN ACCESSSlide46
Web Application
Recruitment
Natural mortality
Fishing mortality
Selectivity
Initial Abundance VectorSlide47
Web Application
www.recuperemoslamerluza.cl
Para recuperar su contraseña
ingresa aquí
Login:
Contraseña:
Enviar
Registrar
Iniciar Sesión
Report generator
Access to previous consults
Workshops information and results
User
Profile
Recovery Plan
Analysis under conditions entered by userSlide48
Web Application
The user selects the year to start analysis
The application uses the respective estimated abundance vector
TOTAL BIOMASS LEVEL COMPARISON FROM ESTIMATED ABUNDANCE VECTORS
2011
N
0
Error on estimation
The user can select an error level on estimated abundance vector
0%
e N
0
-10%
-5%
0%
5%
10%
2002 2003 2004 2005 2006 2007 2008 2009 2010
2011
Natural mortality
Initial Abundance Vector
Selectivity
User Requirements
RecruitmentSlide49
Web Application
The user selects the year to start analysis
The application uses the respective estimated abundance vector
2002
N
0
Error on estimation
The user can select an error level on estimated abundance vector
-10%
e N
0
-10%
-5%
0%
5%
10%
2002
2003 2004 2005 2006 2007 2008 2009 2010 2011
TOTAL BIOMASS LEVEL COMPARISON FROM ESTIMATED ABUNDANCE VECTORS
Natural mortality
Initial Abundance Vector
Selectivity
User Requirements
RecruitmentSlide50
Web Application
The user selects a population ‘recruitment level’ (a believe about the impact of the recruits)
The application uses the
steepness
factor on a Beverton-Holt stock recruitment relationship
Recruitment level
MEDIUM
HIGH
MEDIUM
LOW
[k*recruits]
SSB [ktonnes]
SPAWNING STOCK BIOMASS VS NUMBER OF RECRUITS
HIGH
MEDIUM
LOW
HIGH
MEDIUM
LOW
[ Dynamic Function]
Natural mortality
Initial Abundance Vector
Selectivity
User Requirements
RecruitmentSlide51
Web Application
The user selects an exploitation pattern
From database or logisitic curve
Exploitation pattern from database
Exploitation pattern from logistic curve
EXPLOITATION PATTERN
SELECTIVITY
AGE
2 3 4 5 6 7 8 9 10 11 12 13
1.0
0.0
a
50%
8
11
a
95%
EXPLOITATION PATTERN
SELECTIVITY
AGE
2 3 4 5 6 7 8 9 10 11 12 13
1.0
0.0
0.95
0.50
Natural mortality
Initial Abundance Vector
Selectivity
User Requirements
RecruitmentSlide52
Web Application
Natural mortality
Initial Abundance Vector
Selectivity
User Requirements
Recruitment
Natural Mortality
Without Giant Squid (M = 0.33)
With Giant Squid (M = 0.63)
Other
M
The user enters a natural mortality value depending on the apparition of predators (Giant Squid)
[ Dynamic Function]Slide53
Web Application
ATTENTION
Under actual assumptions it is not possible to take a sustainable yield greater than 32180 [tonnes] or a prevention level for SSB greater than 306650 [tonnes].
To consider,
REQ
≤ 32180 [tonnes]
SSB
min
≤ 306650 [tonnes]
Social required level for yield
[tonnes]
Required SSB prevention level
[tonnes]
User Requirements
Recovery Plan Analysis
Before the user enters data, the application shows thresholds for the user requirements, based on the scenario formulated from previous stages
User RequirementsSlide54
If the requirements are compatible, the application can start with the recovery plan analysis.
Web Application
RECOVERY PLAN ANALYSIS
Under actual assumptions, every recovery plan evaluated needs not less than 2 years of implementation.
ATTENTION
Under actual assumptions it is not possible to take a sustainable yield greater than 32180 [tonnes] or a prevention level for SSB greater than 306650 [tonnes].
To consider,
REQ
≤ 32180 [tonnes]
SSB
min
≤ 306650 [tonnes]
Social required level for yield
30000
[tonnes]
Required SSB prevention level
[tonnes]
116000
User Requirements
User Requirements
Recovery Plan AnalysisSlide55
Web Application
Recovery
Plan
Recovery Plan Proposal
The analysis suggest to consider a TAC of
23.6 [ktonnes]
during
4 [years]
to recover the fishery.
This alternative minimize the cost with a 6.4 [ktonnes] tradeoff per year.
This leads to a total cost of 25.6 [ktonnes] during the entire period (4 years).
Y
2011 2012 2013 2014 2015 2016 2017 2018
30.0 [ktonnes]
23.6 [ktonnes]
Sustainable Fishery
SSB
2011 2012 2013 2014 2015 2016 2017 2018
116.0 [ktonnes]
YIELDS/LANDINGS PER YEAR
RESPECTIVE SPAWNING STOCK BIOMASS LEVELS PER YEAR
Recovery Plan
TAC associated with the minimal cost recovery plan
Landings for ‘healthy fishery’ equal to
REQ
Projection with a constant landing level equal to
REQ
Social required level for yield by user
(
REQ
)
Required SSB prevention level by user
(
SSB
min
)
Recovery Plan Proposal Effects Slide56
Web Application
Dissatisfaction level
(Total costs associated)
Social required level for yield by user (REQ)
TAC associated with
the respective recovery plan
TAC associated with
the minimal cost recovery plan
POSSIBLE RECOVERY PLANS
Implementation years to recovery
30.0 [ktonnes]
23.6 [ktonnes]
2 3 4 5 6 7 8 9 10
Recovery
Plan
Alternative
Recovery PlansSlide57
Transfering
…
Our web application can be used freely
However, this version has some limitations that can be improved together with the stakeholders if needed
We expect this tool can be useful for artisan fishermenSlide58
www.recuperemoslamerluza.cl
More details about the project in
MABIES – IHP - 2013
Quantitative tools for the sustainable
recovery
of the hake (
Merluccius Gayi Gayi
) in the Region
of
Valparaiso, Chile
Thanks!Slide59
[ Natural Mortality]
Theory
Dynamic function and
Optimization Problem
DIFFERENCE EQUATION
BASIC IDEAS
OPTIMIZATIONPROBLEM
DYNAMIC FUNCTION
:
Discount factor
[ Recruitment]
[ Recovery Problem]