February 6, 2013 - Institut Henri Poincaré – Paris - France

February 6, 2013 - Institut Henri Poincaré – Paris - France

Mathematics of Bio-Economics (MABIES)

Quantitative tools for the sustainable recoveryof the hake (Merluccius Gayi Gayi) in the Regionof Valparaiso, Chile

Project started at August, 2011Duration 1.5 yearCurrent Stage Online tool on final development stageProject website www.recuperemoslamerluza.clFinancial 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.

http://www.recuperemoslamerluza.cl/

ResearchTeam

Multidisciplinary Group

Marine Biologists

Engineers

Applied Mathematicians

Expert on social behavior

Journalist

PEDROGAJARDO

HÉCTORRAMÍREZ

ALEJANDROZULETA

DARÍORIVAS

RENZOTASCHERI

MAXIMILIANOOLIVARES

RESEARCHER ONMATHEMATICALMODELLINGPROJECT DIRECTOR

RESEARCHER ON FISHERIESMANAGEMENT

RESEARCHER ONFISHERIES STOCKASSESMENT

MARINEBIOLOGIST

MATHEMATICALENGINEERINGSTUDENT

COLLABORATORSGILDA MEDINA | JOURNALISTHÉCTOR TRUJILLO | SOFTSYSTEMS ANALYSIS GROUP (VENEZUELA)ANGGELO URSO | COMPUTER ENGINEERING

RESEARCHER ONMATHEMATICALMODELLINGADJOINT DIRECTOR

Oldest and most important demersal fishery in Chile

Main fishery resource of the Region of Valparaiso

HakeFishery

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

GIANTSQUID

HakeFishery

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

HakeFishery

The aim of this project is to provide quantitative tools to propose recovery strategies for this fishery

Stakeholders

Stakeholders

Yields Landings / catches

Stakeholders

Yields

Prevention

Landings / catches SSB SpawningStock Biomass

Stakeholders

Yields Landings / catches

Prevention

SSB SpawningStock Biomass

SocialRequirement

Level of yields required by the local community


Stakeholders


Yields

SocialRequirement

Prevention


Stakeholders

YieldsPrevention

SocialRequirement

Recovery Plan Proposal



Stakeholders

YieldsPrevention

BIOLOGICAL INDICATORS Spawning Stock Biomass Total Biomass

SocialRequirement




Stakeholders

YieldsPrevention


ECONOMICAL INDICATORS Landings Economical return of the fleets

SocialRequirement




Stakeholders

YieldsPrevention


ECONOMICAL INDICATORS Landings Economical return of the fleets

The plan will be optimal in some predefined sense

SocialRequirement



Stakeholders

Meetings with stakeholders


Stakeholders

To introduce the project To obtain feedback


Stakeholders

To introduce the project To obtain feedback

Bottom-up relation with the different actors involved in the fishery management

Stakeholders

3 Stages

Visiting local fishing baysStage I

Interviews with stakeholders in theRegion of Valparaiso

Stage II

“Identifying the main problems for the recovery of hake”

Stage III WORKSHOP

Stakeholders

3 Stages


Interviews with stakeholders in the Region of Valparaiso

Stage II


Stage III WORKSHOP

Stakeholders

3 Stages



Stage II


Stage III WORKSHOP

Eduardo Quiroz“Portales”

Miguel Ángel Hernández“Puertecito”

Gabriel Valenzuela“El Membrillo”

Valparaíso

Valparaíso

San Antonio

Stakeholders

3 Stages



Stage II


Stage III WORKSHOP

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 theexploitation of the hake fishery

THEORY

WORKSHOPS &STAKEHOLDERS

RESEARCHTEAM

FISHERIES STOCK

ASSESSMENT

WEBWAREWEB APPLICATION

OPEN ACCESS

Technological Transfer


OPEN ACCESS

THEORY


RESEARCHTEAM

FISHERIES STOCK

ASSESSMENT



THEORY


RESEARCHTEAM

FISHERIES STOCK

ASSESSMENT


OPEN ACCESS

TheoryBASIC IDEAS

TheoryBASIC IDEAS

FISHERIES DATAESTIMATION

MEANWEIGHT + OTHERS

ABUNDANCEESTIMATION

TheoryBASIC IDEAS

FISHERIES DATAESTIMATION

MEANWEIGHT + OTHERS

ABUNDANCEESTIMATION

N ABUNDANCE VECTOROR STATE

TheoryBASIC IDEAS

INITIAL STATEN0

TheoryBASIC IDEAS

Y

t

N0

Yields | Landings | Catches

[kto

nnes

]

[years]

FROM

t 0

Yields from some strategy

…INITIAL STATEN0

TheoryBASIC IDEAS

Y

t

N0

[kto

nnes

]

[years]

FROM

t 0

… ymin

INITIAL STATEN0

We focus on minimal sustainable value for yield


ymin

TheoryBASIC IDEAS

N0

FROM

INITIAL STATEN0

We seek strategies which ensures instead of

…

Y

t

ymin[kto

nnes

]

[years]

N0

FROM

…

Y

t

ymin[kto

nnes

][years]

ymin

as minimal sustainable value for yield

ymin

By modifying the exploitation strategy

ymin

TheoryBASIC IDEAS

INITIAL STATEN0

ymin

ymin?

What is the maximum possible value for ymin?

…

Y

t

ymin[kto

nnes

]

[years]

yminMm

ymin

N0

FROM


TheoryBASIC IDEAS

INITIAL STATEN0

N0

FROM

MmWe can use this value to propose a recovery plan

Mm

ymin


TheoryBASIC IDEAS

INITIAL STATEN0

N0

FROM

Mm

Recovery Problem

MmMaximum possible value for ymin

TheoryBASIC IDEAS

INITIAL STATEN0

N0

FROM

Mm

Mm Maximum possible value for ymin

REQ

Recovery Problem

REQSocial required level for yield

TheoryBASIC IDEAS

INITIAL STATEN0

N0

FROM

Mm


REQ Social required level for yield

REQ

Recovery Problem

What strategy can be used to pass from N0 to a “healthy” fishery N(T)?

N0 N(T)

TheoryBASIC IDEAS

INITIAL STATEN0

N(T)FROM

Mm

REQ

Recovery Problem


REQ Social required level for yield N0 N(T)What strategy can be used to pass from N0 to a “healthy” fishery N(T)?

TheoryBASIC IDEAS

INITIAL STATEN0

N(T)FROM

Mm



REQ

Recovery Problem


N0 N(T)

TheoryBASIC IDEAS



RECOVERYPLAN

REQ REQ

Mm

Mm

T yearsConstant Total Allowable

Catches (Yields)

N(T)N0

Recovery Problem


N0 N(T)


REQ Social required level for yield SSB Mínimum value for SSB according Mm SSBmin Required SSB prevention level

TheoryBASIC IDEAS

REQ REQ

Mm

Mm

N(T)N0

Recovery Problem

SSB

SSB

RECOVERYPLANT yearsConstant TAC (Yields)

SSBmin

SSBmin


N0 N(T)

TheoryBASIC IDEAS

RECOVERYPLAN

REQ REQ

Mm

Mm

T yearsConstant TAC (Yields)

N(T)N0

Recovery Problem

SSB

SSB

TRADEOFF:COST= REQ-TAC

OPTIMIZATION PROBLEM:WHAT IS THE RECOVERYPLAN WITH MINIMAL COST?

SSBmin

SSBmin


REQ Social required level for yield SSB Mínimum value for SSB according Mm SSBmin Required SSB prevention level


N0 N(T)

[ Dynamics and Optimization Problem]


THEORY


RESEARCHTEAM

FISHERIES STOCK

ASSESSMENT


OPEN ACCESS

Web Application

Recruitment

Natural mortality

Fishing mortality

Selectivity

Initial Abundance Vector

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

UserProfile

Recovery PlanAnalysis under conditions entered by user

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

2011N0

Error on estimation→ The user can select an error level on estimated

abundance vector

0%e N0-10%-5%0%5%10%

2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

Natural mortality

Initial Abundance Vector Selectivity

User Requirements

Recruitment

Web Application

The user selects the year to start analysis→ The application uses the respective estimated

abundance vector

2002N0

Error on estimation→ The user can select an error level on estimated

abundance vector

-10%e N0-10%-5%0%5%10%

2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

TOTAL BIOMASS LEVEL COMPARISON FROM ESTIMATED ABUNDANCE VECTORS

Natural mortality


User Requirements

Recruitment

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

HIGHMEDIUMLOW

[k*recruits]

SSB [ktonnes]

SPAWNING STOCK BIOMASS VS NUMBER OF RECRUITS

HIGHMEDIUM

LOW

HIGH

MEDIUMLOW

[ Dynamic Function]

Natural mortality


User Requirements

Recruitment

Web Application

The user selects an exploitation pattern

→ From database or logisitic curve

Exploitation pattern from database Exploitation pattern from logistic curve

EXPLOITATION PATTERN

SELE

CTIV

ITY

AGE

2 3 4 5 6 7 8 9 10 11 12 13

1.0

0.0

a50% 8

11a95%

EXPLOITATION PATTERN

SELE

CTIV

ITY

AGE

2 3 4 5 6 7 8 9 10 11 12 13

1.0

0.0

0.95

0.50

Natural mortality


User Requirements

Recruitment

Web Application

Natural mortality


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]

Web Application

ATTENTIONUnder 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] SSBmin ≤ 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 Requirements

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.

ATTENTIONUnder 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] SSBmin ≤ 306650 [tonnes]

Social required level for yield 30000 [tonnes]

Required SSB prevention level [tonnes]116000

User Requirements

User Requirements

Recovery Plan Analysis

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 (SSBmin)

Recovery Plan Proposal Effects

Web Application

Dissatisfaction level (Total costs associated)

Social required level for yield by user (REQ)

TAC associated withthe respective recovery plan

TAC associated withthe 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 Plans

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 fishermen

www.recuperemoslamerluza.clMore details about the project in

MABIES – IHP - 2013

Quantitative tools for the sustainable recoveryof the hake (Merluccius Gayi Gayi) in the Regionof Valparaiso, Chile

Thanks!

[ Natural Mortality]

Theory Dynamic function andOptimization Problem

DIFFERENCE EQUATION

BASIC IDEAS

OPTIMIZATIONPROBLEM

DYNAMIC FUNCTION

: Discount factor

[ Recruitment][ Recovery Problem]

February 6, 2013 - Institut Henri Poincaré – Paris - France

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