Modeling Fisheries and Environmental Management Problems by Bayesian Methods

Modeling Fisheries and

Environmental Management

Problems by Bayesian Methods

Sakari Kuikka,

Fisheries and Environmental Management Group

University of Helsinki

Outline of the talk

1) FEM group and some projects

2) Bayesian inference & Bayesian

nets

3) Fisheries modelling: Experiences

in PRONE, JAKFISH and

FEM group (Helsinki

●

, Kotka ●,

Oulu

●

Turku

X

)

• Professori Sakari Kuikka:Johtaa, päätösanalyysi ● ●

• FT (tilastot.) Samu Mäntyniemi: Bayesläinen tilastotiede, riskilaskenta ●

• FT Eveliina Linden: ECOKNOWS, ryhmän koordinointi, varajohtaja ●

• MMT (biol.) Mika Rahikainen: kalastuksen säätely, kalastusekonomia ●

• TkT Jarno Vanhatalo: Bayes laskenta-algioritmit, kaikuluotaus ●

• FM, DI Inari Helle: öljyonnettomuuksien riskianalyysi , IBAM ●

• FM, DI Teppo Juntunen: Bayeslaskenta, PROBAPS ●

• FM Annukka Lehikoinen: teknis-biologiset riskimallit, Suomenlahden tila ●

• FM (sosiol.) Päivi Haapasaari: kalastussosiologia ●

• FM (tilastotiede) Henni Pulkkinen, Oulu, ECOKNOWS ja muu rahoitus ●

• FM Clarence Gonzales (cross displinary fisheries), IBAM ja JAKFISH ●

• FM (maantiede) Emilia Luoma: ekonominen riskianalyysi X

• FM (biologia) Riikka Venesjärvi: alueelliset öljyvahingot ●

Liittoutuminen HY:n tilastotieteen laitoksen kanssa (Prof. Jukka Corander)in ryhmä

SA

F

GOF

OI

L

R

ISK

PROB

A

PS

IB

A

M

P r o j e c t s

Accident probabilities Drift calculations

SAFGOF model: results

Distributions for endangered species

SAFGOF model: results Clean-up costs

(shore)

Risk estimates

Costs of reed: WTP

Costs of reed: estate values

Fucus model: results

Reed model: results

Endangered species model: results Value of endangered species Climate modelling Eutrophication modelling

Sources of uncertainty

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Predicted SSB Pr o b a b il ity Implementation Parameters Model Natural

By Samu Mäntyniemi, FEM Critical

limit

Bayesian inference: updating knowledge

Initial knowledge

Pre-defined interpretation

of evidence

New evidence

Updated knowledge

“Prior”, before evidence

“Likelihood”

“Posterior”, after evidence

FACTS

BELIEFS/ASSUMPTIONS

Bayes rule: probabilistic

dependencies

Real number

of fish (B)

Observations

(data), A

Observations

Real number

of fish (B)

Classical:

P (A|B)

Bayes:

P (B|A)

0 0,05 0,1 0,15 0,2 0,25 1 3 5 7 9 11 13 15 17 19 21 23 25 p ro b a b il ity Population size (N) P(N) P(data|N) P(N|data)

Prior

Likelihood

Posterior

•

: true weight

• Prior : mean=70, sd=4

•

: weight measurement

• Measurement model: the scale is

not very good. Expected

measurement = true weight,

uncertainty: sd=1 kg

• Observation

• How to interpret this regarding the

true weight?

Simple example: estimation of

weight

μ

x

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 62 64 66 68 70 72 74 True weight 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 62 64 66 68 70 72 74 Observed weight

Data: x=68

P (dat a | t rue w e ight)

Likelihood(true weight | data=68)

”Posterior



Likelihood x Prior”

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 62 64 66 68 70 72 74 p (x = 6 8 |m u ) mu

Informative data, uninformative prior _{Uninformative data, informative prior}

Uninformative data, uninformative prior

Highly uninformative data & unformative prior

Samu Mäntyniemi, FEM

State of nature Knowledge

Action New state of

nature

Production potential of the stock (real state of nature)

How well we can measure/assess ? = quality of the science

Available knowledge

How strong will be the impact

of decision on nature (e.g. implementation uncertainty)

= aim

Utility: dependent on action and on the real state of nature

BBN: Chains of knowledge and actions

Fisheries

PRONE (past project)

Hierarchical S/R analysis

• Learning from closeby populations

• Essential methodology for e.g. threatened

species

Stock-recruitment estimates (data)

0.0 0.5 1.0 1.5 2.0 0 10 20 30 40 North Sea SSB in 10^6 of t R e c ru its in 1 0 ^9 o f fis h 0.0 0.5 1.0 1.5 2.0 2.5 0 10 20 30 40 Baltic SSB in 10^6 of t R e c ru its in 1 0 ^9 o f fis h 0 5 10 15 0 50 150 250 Norwegian SSB in 10^6 of t R e c ru its in 1 0 ^9 o f fis h 0.1 0.2 0.3 0.4 0.5 0 2 4 6 8 Celtic SSB in 10^6 of t R e c ru its in 1 0 ^9 o f fis h 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0 .2 0 .4 0 .6 0 .8 Irish North SSB in 10^6 of t R e c ru its in 1 0 ^9 o f fis h 0.05 0.10 0.15 0.20 0.25 0.30 0 .5 1 .5 2 .5 Irish South SSB in 10^6 of t R e c ru its in 1 0 ^9 o f fis h

Hierarchical Bayesian model

No hierarchy

PRONE PROJECT: Hillary et al. 2009

JAKFISH project: unpublished

results

Modelling different causalities

By

2

1

Population

size ?

Catch

Survey

Growth

Size and

age

Natural mortality?

Fishing mortality?

Recruitment?

Heart of stock assessment:

population dynamics model

• Describes how a population changes over

time

• Constraints

– Length of fish can only increase

– Abundance of a year class can only get smaller

– Number of spawned eggs restricts the number of

Number of mature individuals in each age % mature at age Number of eggs spawned Weight at age Fecundity at weight Stock-recruitment relationship R #eggs Natural mortality Fishing mortality: Availability Selectivity Growth Individual size Stakeholder knowledge Stakeholder knowledge Stakeholder knowledge

• Fishbase: large database of fish biology

– Length-weight relationship

– Growth parameters

• Scientific literature

– Relative fecundity of herring

– Natural mortality of fish based on length

– Survival of eggs

• Knowledge of 6 stakeholders

– Factors affecting the variation of growth, survival

of eggs and natural mortality

Prior information about population

dynamic parameters

• Standard ICES input (1974-2007)

– Commercial catch at age

– Weight at age in stock & catch

– Survey catch per unit of effort at age

– Maturity at age

– Input: biomass and age distribution separately

• Sample size of age determination data

• Estimate of sampling variation in total catch

in biomass

– Cod biomass

– Sprat biomass

– Zooplankton density

– Sea surface temperature

– Salinity

– Water transparency (Secci depth)

Data on factors indentified by

stakeholders

Example: Factors affecting natural mortality - a

causal model

Natural mortality Cod abundance Seals etc Parasites, diseases Mean zooplankton pseudocalanus Others: 30% 50% 5% 5% 5% 5% 5% 5% + + + -

-• Stock assessment using views of stakeholder 1

– Purpose

• show the various outputs

• Visualize the amount of uncertainty in the estimates

• Comparisons of all stakeholders

– Showing only expected values

– Uncertainty is difficult to visualise in comparisons

Results

Biomass and catch: Fishing effort

as in 2007

Strong year classes predicted for 2007 & 2008

Fishing & natural mortality: Effort

as in 2007

Zooplankton

Cod

Eggs & recruits

: Effort as in 2007

Comparisons: eggs-recruits

Temperature Secci depth Temperature Cod Zooplankton Stakeholder=1 Stakeholder=6

Comparisons: Mortalities Stakeholder=1 Stakeholder=6 Cod Zooplankton Cod Zooplankton

Comparisons: Closing the fishery

Fishing mortality Natural mortality Biomass

Comparisons: no change in effort

compared to 2007

3

5

Fishing mortality Natural mortality Biomass

Weights: different areas of

expertise

SH Growth Prob. Natural mortali ty

Prob. Recruitment Prob.

1 Zoopl,Temp, Salinity 0. Zoopl,C od 0 Temp,Secci 0.0042 2 Zoopl,Salinity, Sprat

0.0086 Cod 0.00006 Temp, Cod, Sprat, Salinity

0.0236

3 Zoopl,Sprat

_0.0202

Cod

_0.0070

Temp

_0.035

4 Zoopl,Temp 0.00013 Cod

_0.989

Zoopl, Secci 0.00001 5 Zoopl,Temp, Salinity 0.017 Cod,Zo opl 0.00313 Cod 0.0018 6 Zoopl,Temp, Salinity,Sprat

0.953

Cod,Zo opl 0 Temp,Cod,Zoopl

_0.934

Weights: single stakeholder is best

in all areas

SH Growth Natural

mortality

Recruitment Probability

1 Zoopl,Temp,Salinity Zoopl,Cod Temp,Secci 0.0000001

2 Zoopl,Salinity,Sprat Cod Temp, Cod, Sprat, Salinity

0.0015

3 Zoopl,Sprat Cod Temp

_0.98

4 Zoopl,Temp Cod Zoopl, Secci 0.0007 5 Zoopl,Temp,Salinity Cod,Zoopl Cod

_0.0126

6 Zoopl,Temp,Salinity,

Sprat