jeffrey dambacher & keith hayes csior mathematical and information sciences

Linking Threats to Assets in Complex Ecological and Socio-Economic Systems: Qualitative Modelling for Tourism Development in North Western Australia

Jeffrey Dambacher & Keith HayesCSIOR Mathematical and Information Sciences

Geoff HosackOregon State University

Risk-Based Management of Natural Resources

• Depends on models• Risk assessment predicated on model linking threats to asset

• Natural systems are complex• Realistic representation of causality is difficult• Ecological and socioeconomic systems have feedback

• Experts versus stakeholder participation• Stakeholders typically not involved in model development yet live with the risk

• Model uncertainty• Difficult to address

• Results conditional on all parameters• Typically a narrow field of models considered

Threat AssetModel

Model Uncertainty

Parametric Uncertainty• Precise measurements• Expert opinion• Simulations with plausible parameter space• Receives majority of attention and effort in modelling

Model Structure Uncertainty• Within a model: feedback cycles with opposing sign• Between models: different interactions or variables• Largely ignored

“Model structure uncertainty is the 800 pound gorilla in

the middle of the room that no-one talks about”

Scott Ferson

Methods

• Causal Graphical Models

• Bayesian belief network (BBN)

• Qualitative model (QM)

• Model uncertainty

• Qualitative Prediction weights

• Merging of BBN and QM

Bayesian Belief Networks

• group of nodes connected by directed arrows such that there are no cycles (loops)

• “child” nodes with incoming arrows are probabilistically dependent on “parents” values

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X2 X3

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Qualitative ModellingQualitative Modelling

CCOMMUNITY OMMUNITY MMATRIXATRIXCCOMMUNITY OMMUNITY MMATRIXATRIX

SIGNED DIGRAPHSSS IGNEDIGNED DD IGRAPHSIGRAPHS

PREDATOR-PREYPPREDATORREDATOR--PPREYREY

MUTUALISMMMUTUALISMUTUALISM

COMMENSALISMCCOMMENSALISMOMMENSALISM

COMPETITIONCCOMPETITIONOMPETITION

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SELF-EFFECTSSELFELF--EFFECTEFFECT

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Press Press PerturbationsPerturbationsPress Press PerturbationsPerturbations

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Krebs et al. (1995) ExperimentKrebs et al. (1995) Experiment

• Hare food addition: hares increased

• Predator exclosures: hares increased

• Food and exclosures: hare increase multiplicative

• Fertilization: vegetation increased, hares neutral ?

• Hare food addition: hares increased

• Predator exclosures: hares increased

• Food and exclosures: hare increase multiplicative

• Fertilization: vegetation increased, hares neutral ?

V H PV H P

V H PV H P

Positive InputPositive InputVVEG.EG. H HAREARE P PRED.RED.

Positive InputPositive InputVVEG.EG. H HAREARE P PRED.RED.

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MMODELODEL A AMMODELODEL A A

MMODELODEL B BMMODELODEL B B

VVEG.EG.

HHAREARE

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ResponseResponseVVEG.EG.

HHAREARE

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ResponseResponseVVEG.EG.

HHAREARE

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CCRITICALRITICAL E EXPERIMENTXPERIMENTCCRITICALRITICAL E EXPERIMENTXPERIMENT

Qualitative Prediction WeightsQualitative Prediction Weights

Impact to CoralImpact to Coral from Input to Algae from Input to Algae 358 feedback cycles 358 feedback cycles + 82, - 276, 194 net + 82, - 276, 194 net Prediction weight Prediction weight W = 194/276 = 0.54 W = 194/276 = 0.54

Negative response Negative response in coral seems in coral seems likely....likely....but how likely?but how likely?

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Prediction Weight Wi j

Testing prediction weights (W) through simulations

• Proportion of simulations with correct sign given by least square fit to non-linear function

• Sign of each element of adj(–ºA) converted into a probability and incorporated into the CPTs of a BBN via a linear relationship

Qualitative predictions to CPT

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Snowshoe hare example

Model A Model B

Sym_Adj (-°A) Sym_Adj (-°B)

Adj (-°A) W Adj (-°B) W

The null model = fully connected community matrix

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a ,1 2 a ,2 3 a ,1 3 a ,2 2

a ,2 1 a ,3 3 a ,2 3 a ,3 1 a ,1 1 a ,3 3 a ,1 3 a ,3 1

a ,1 1 a ,2 3 a ,1 3 a ,2 1

a ,2 1 a ,3 2 a ,2 2 a ,3 1 a ,1 1 a ,3 2 a ,1 2 a ,3 1

a ,1 1 a ,2 2 a ,1 2 a ,2 1

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Snowshoe hare CPT

Model Incr(Veg) Incr(Veg) Unch(Veg) Decr(Veg) Incr(Hare) Unch(Hare) Decr(Hare) Incr(Lynx) Unch(Lynx) Decr(Lynx)A Incr 0.96 0.02 0.02 0.96 0.02 0.02 0.96 0.02 0.02A Unch 0.02 0.96 0.02 0.02 0.96 0.02 0.02 0.96 0.02A Decr 0.02 0.02 0.96 0.02 0.02 0.96 0.02 0.02 0.96B Incr 0.96 0.02 0.02 0.33 0.33 0.33 0.96 0.02 0.02B Unch 0.02 0.96 0.02 0.02 0.96 0.02 0.02 0.96 0.02B Decr 0.02 0.02 0.96 0.33 0.33 0.33 0.02 0.02 0.96

Null Incr 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33Null Unch 0.02 0.96 0.02 0.02 0.96 0.02 0.02 0.96 0.02Null Decr 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33

Snowshoe hare BBN

Lynx

IncreaseUnchangedDecrease

80.59.739.73

Snowshoe_hare

IncreaseUnchangedDecrease

0 100 0

Vegetation

IncreaseUnchangedDecrease

100 0 0

Alternative_models

ABNull

4.2671.124.7

Input_to_Veg

IncreaseUnchangedDecrease

100 0 0

Ningaloo Project Objectives

• Qualitative models of ecosystem and socio-economic system with tourism impacts in a marine park

• Complement quantitative modelling• Integrative framework for expert and

stakeholder knowledge• Evaluate management strategies

-

+

Increasednutrients

+

+

+

Increasedharvest

-

monitoring

management

Monitoring and management add two negative feedback cycles

Management problem: trophic cascade effects of recreational fishing

Coral Reef ModelCoral Reef Model

Netica Example

Monitoring and management add 1026 feedback cycles

Coral Reef ModelCoral Reef Model

Thank you