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Becky Epanchin-Niell Jim Wilen Prepared for the PREISM workshop ERS Washington DC May 2011

Optimal Management of Established Bioinvasions. Becky Epanchin-Niell Jim Wilen Prepared for the PREISM workshop ERS Washington DC May 2011 . Bioinvasions Are: Spatial-dynamic Processes. Spatial-dynamic processes are driven by dynamics at a point and diffusion between points

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Becky Epanchin-Niell Jim Wilen Prepared for the PREISM workshop ERS Washington DC May 2011

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  1. Optimal Management of Established Bioinvasions Becky Epanchin-Niell Jim Wilen Prepared for the PREISM workshop ERS Washington DC May 2011

  2. Bioinvasions Are:Spatial-dynamic Processes • Spatial-dynamic processes are driven by dynamics at a point and diffusion between points • Generate patterns that evolve over both space and time • Some other examples • Forest fires • Floods • Aquifer dynamics • Groundwater contamination • Wildlife movement • Human/animal disease

  3. Questions raised by bioinvasions: • How does uncontrolled invasion spread? • Intensity and timing of optimal controls • when and how much control? • Spatial strategies for control • Where should control be applied? • Effect of spatial characteristics of the invasion and landscape on optimal control • Externalities, institutions, and reasons for intervention

  4. Modeling Optimal Bioinvasion Control with Explicit Space • Simple small model • Build intuition with multiple optimization “experiments” • Identify how space matters with spatial-dynamic processes • Explore how basic bioeconomic parameters affect the qualitative nature of the solution

  5. Special (Spatial) Modeling Issues boundaries heterogeneity spatial geometry diffusion process

  6. The model • Invasion spread • Cellular automaton model • Approximates reaction-diffusion • Control options • Spread prevention • Invasion clearing • Min. total costs & damages • Simplicity • - 2n*t configurations invadable land invaded land ($d) border control ($b) clearing ($e)

  7. Finding the optimal solution • Dynamic problems • Ordinary differential equations • End-point conditions—2 point boundary prob. • Spatial-dynamic problems • Partial differential equations • End-points---infinite dimension spatial bound. • difficult/impossible to analytically solve

  8. Finding the optimal solution Dynamic programming solutions • Backwards recursion • Curse of dimensionality amplified • Number of states/period • Additional problems • Eradicate vs. slow or stop solutions • Transversality conditions

  9. Mathematical model spread preventioncosts clearingcosts damages Subject to: Cell remains invaded unless cleared Cell becomes invaded if has invaded neighbor unless prevention applied parameters variables

  10. Solution approach: • Binary integer programming problem • - SCIP (Solving Constraint Integer Programs) • Scaling • Solves large-scale problems in seconds/minutes • Can perform numerous comparative spatial-dynamic optimization “experiments” • Cost parameters, discount rate • Invasion and landscape size • Invasion and landscapes shape • Invasion location

  11. Results: • Wide range of control approaches • e.g., eradicate, clear then contain, slow then contain, contain, slow then abandon, abandon • If clearing is optimal, it is initiated immediately • Landscape & invasion geometry important • Spatial strategies for control • prevent/delay spread in direction of high potential damages • reduce extent of exposed edge prior to containment • whole landscape matters

  12. Experiment 1: Initial invasion size • Finding: Larger invasion decreases optimal control • Reason: Larger invasion  higher control costs & less uninvaded area to protect • Invasion size = Control delay

  13. Experiment 1: Initial invasion size • Larger delay  higher total costs and damages Total (optimized) costs & damages

  14. Experiment 2: Landscape size • Finding: Larger landscapes demand greater levels of control • Reason: Larger uninvaded areas  Higher potential long-term damages

  15. Experiment 3: Landscape shape • Finding: Higher optimal control effort in more compact landscapes • Reason: Damages accrue faster  Higher long-term potential damages in more compact landscapes

  16. Experiment 4: Invasion location • Central invasions • - higher potential long-term damages •  more control • Invasions near range edge • - lower control costs •  more control Invasion location has ambiguous effect on optimal control effort Central invasions  higher costs & damages

  17. Spatial control strategies I: • Prevent spread in direction of high potential long-term damages • Reduce the extent of invasion edge prior to containment t = 0 t = 6… t = 3 t = 1 t = 2 t = 4 t = 5

  18. Spatial control strategies II: • Reduce the extent of invasion edge • Protect areas with high potential damages t = 0 t = 6… t = 3 t = 1 t = 2 t = 4 t = 5

  19. Spatial control strategies III: t = 0 t = 1 t = 2 t = 3… Again, reduce invasion edge prior to containment. 11  7 edges exposed

  20. Spatial control strategies IV: t = 0 t = 6… t = 3 t = 1 t = 2 t = 4 t = 5

  21. Spatial control strategies V: Protect large uninvaded areas Entire landscape matters t = 9 t = 0 t = 6 t = 3 t = 1 t = 2 t = 4 t = 5 t = 7 t = 8

  22. If landscape homogeneous No control… let spread Barrier cost (b) = 50 Removal cost (e) = 1500 Baseline damages (d) = 1

  23. If high damage patch in landscape  Eradicate Barrier cost (b) = 50 Removal cost (e) = 1500 Baseline damages (d) = 1 High damages (d) = 101 t = 6 t = 7 t = 8 t = 1 t = 0 t = 3 t = 4 t = 5 t = 2

  24. If higher removal costs  Slow spread; protect high damage patch Barrier cost (b) = 50 Removal cost (e) = 10000 Baseline damages (d) = 1 High damages (d) = 101 t = 6 t = 7 t = 8 t = 0 t = 11 t = 3 t = 1 t = 4 t = 5 t = 2 t = 10 t = 14 t = 17… t = 12 t = 16 t = 15 t = 9 t = 13

  25. If lower damages in patch Slow the spread Barrier cost (b) = 50 Removal cost (e) = 10000 Baseline damages (d) = 1 High damages (d) = 51 t = 6 t = 7 t = 8 t = 0 t = 11 t = 3 t = 1 t = 5 t = 4 t = 2 t = 10 t = 12 t = 9 t = 13…

  26. Summary of control principles • High damages, low costs, and low discount rate,  higher optimal control efforts • Protect large uninvaded areas • prevent/delay spread in direction of high potential damages • Reduce extent of exposed edge prior to containment • employ landscape features • alter shape of invasion (spread, removal) • Entire invasion landscape matters • Geometry matters (initial invasion, landscape) • Control sequences/placement can be complex

  27. Modeling multi-manager landscapes invaded about to be invaded adjacent to “about to be invaded” Offer to “about to be invaded” cell to induce prevention • Unilateral management • Bilateral bargaining • Local “club” formation

  28. Outcomes from private control vs. optimal control: Clearing cost (e) Unilateral management Bilateral bargaining Local “club” coordination Border control cost (b) Optimal control Clearing cost (e) Border control cost (b)

  29. Thank you!!

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