Jeffrey Dambacher & Keith Hayes CSIOR Mathematical and Information Sciences

1. Linking Threats to Assets in Complex Ecological and Socio-Economic Systems: Qualitative Modelling for Tourism Development in North Western Australia Jeffrey Dambacher & Keith Hayes CSIOR Mathematical and Information Sciences Geoff Hosack Oregon State University

2. Risk-Based Management of Natural Resources Asset Threat • 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 Model

3. 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

4. “Model structure uncertainty is the 800 pound gorilla in the middle of the room that no-one talks about”Scott Ferson

5. Methods • Causal Graphical Models • Bayesian belief network (BBN) • Qualitative model (QM) • Model uncertainty • Qualitative Prediction weights • Merging of BBN and QM

6. X1 X1 X2 X3 X2 X3 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

7. Qualitative Modelling SIGNED DIGRAPH COMMUNITY MATRIX -α1,2 -α1,2 0 0 0 A = +α2,1 +α2,1 0 0 0

9. Press Perturbations

10. Effect to 2 from positive input to 1 a3,1 a2,1 a2,3 a3,3

11. Krebs et al. (1995) Experiment • Hare food addition: hares increased • Predator exclosures: hares increased • Food and exclosures: hare increase multiplicative • Fertilization: vegetation increased, hares neutral ?

12. CRITICAL EXPERIMENT Positive Input VEG. HARE PRED. MODEL A - + + - + 0 VEG. HARE PRED. Response VEG. HARE PRED. + - + + - + + + + + 0 + MODEL B

13. Qualitative Prediction Weights • Impact to Coral from Input to Algae 358 feedback cycles + 82, - 276, 194 net Prediction weight W = 194/276 = 0.54 Negative response in coral seems likely.... but how likely?

14. Testing prediction weights (W) through simulations

15. Qualitative predictions to CPT • 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

16. Snowshoe hare example Model B Model A Sym_Adj (-°A) Sym_Adj (-°B) Adj (-°A) W Adj (-°B) W

17. The null model = fully connected community matrix Sym_Adj_Null W_Null Adj_Null

18. Snowshoe hare CPT

19. Snowshoe hare BBN

20. 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

21. Management problem: trophic cascade effects of recreational fishing Increased harvest - + management + + Monitoring and management add two negative feedback cycles - + Increased nutrients monitoring

22. Coral Reef Model

23. Netica Example

24. Coral Reef Model Monitoring and management add 1026 feedback cycles

25. Thank you