Cameron Fletcher Andrew Higgins David Hilbert Peter Roebelling

1. Identification of dynamically resilient exploitation-strategies in complex landscape systems using spatially explicit dynamical models and multi-objective optimisation Cameron Fletcher Andrew Higgins David Hilbert Peter Roebelling

2. General understanding of land exploitation as a dynamical system An improved understanding of the trade-offs in land use “triple bottom line”

3. Project objectives 1. Develop an heuristic, phenomenological model of local land-exploitation 2. Using the local model, develop a spatially explicit model of landscape-level land-use 3. Develop techniques for multi-objective optimisation to discover landscape-scale exploitation strategies that are optimal in terms of system-wide dynamical properties such as resilience

4. 4. Identify land-exploitation strategies that lead to the best long-term environmental and socio-economic outcomes as a function of regional environmental and economic characteristics 5. Assess the utility of the multi-objective optimisation techniques in collaboration with other projects

5. A local land-exploitation model based on ecological exploitation models

6. 100 90 80 70 60 N 50 æ ö 40 dN N 30 = - ç ÷ rN 1 20 dt è K ø 10 0 20 40 60 80 100 Time 3 æ ö æ ö dN N N æ ö dH N = - - ç ÷ ç ÷ rN 1 C H 2 = - Consumption ç ÷ aC H bH max + dt K h N è ø è ø max + dt h N è ø 1 Exploitation by predator 0 0 20 40 60 80 100 efficiency consumption mortality K r=.1 K=100 N

7. 50 Prey 49 100 48 90 predator 80 47 150 70 125 46 60 100 50 45 75 0 1 2 3 4 5 6 40 50 30 25 20 0 5 10 15 20 25 30 35 0 0 10 20 30 40 50 60 Dynamics Single point attractor Multiple attractors Stable limit cycle

8. Production function with weak substitutability can be represented by where P is the rate of production C is the rate of exploitation of N and a and b are efficiencies of production using H and Crespectively a b H C = P a + b H C æ ö N = ç ÷ C C H max + è h N ø Land exploitation Define N as aggregate, renewable natural capital Define H as aggregate human-made capital and labour

9. æ ö æ ö dN N N Natural Capital = - - ç ÷ ç ÷ rN 1 C H max + dt K h N è ø è ø a b H C Economic Production = P a + b dH H C = - d sP H dt æ ö N = ç ÷ C C H max + Human-made Capital è h N ø Savings Rate Depreciation Rate

10. H H* dH/dt=0 dH/dt=0 H* dN/dt=0 N N1* Threshold N* N2* N*

11. H economic and environmental constraints agribusiness farming grazing system swidden agriculture N Hunter/Gatherer Strategies in the exploitation state space non-extractive uses Intensification Ecosystem G&S

12. DV1 H Pareto front DV2 N Local optimisation Intensification Ecosystem G&S

13. DV1 Local strategy Pareto front DV2 Subsidies Externalities External Environment Local Model Represent spatial interactions in terms of their effects on natural capital, economic value, and biodiversity

15. Multi-objective optimisation The Multi-objective Optimisation Problem can be defined as finding a vector of decision variables which satisfies constraints and optimises a vector function whose elements represent the objective functions. Having several objective functions, the notion of “optimum” changes, because we are trying to find a set of compromises (a so called Pareto optimum) rather than a single solution as in global optimisation.

16. Report set of best strategies Optimisation using Genetic Algorithms Generate a population of models with random combinations of cmax, h and s Run each model for some number of time steps Calculate the model’s fitness from some (muti-objective) criteria Select some small number of models with the highest fitness, eliminate the rest Generate a new population of models by recombination and mutation

17. Example Fitness=mean production/standard error of N 45000 24 40000 22 35000 20 30000 Pmean N variance 18 25000 16 20000 15000 14 10000 12 5000 10 0 0 10 20 30 40 50 0 10 20 30 40 50 Epoch Epoch 0.12 0.1 0.08 exploitation per unit H 0.06 0.04 0.02 N 0 0 50 100 150 200 250 300

18. 0.06 0.05 0.04 0.03 0.02 0.01 0 0 200 400 600 800 1000 1200 120 100 N 80 60 u=2.0 40 20 0 0 200 400 600 800 1000 1200 120 100 N 80 60 u=2.5 40 20 time 0 0 200 400 600 800 1000 1200 g

19. 80 70 60 50 N* 40 30 20 10 0 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 140 120 100 variance N* 80 60 mean 40 no forcing 20 0 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 u

20. Biophysical environment r sr K Economic environment a b sb C max Exploitation strategy s h Parameters

21. 120 100 80 N 60 120 40 100 N 20 80 60 0 0 200 400 600 800 1000 1200 u=2.0 40 time 20 0 0 200 400 600 800 1000 1200