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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 - PowerPoint PPT Presentation
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Becky Epanchin-NiellJim Wilen
Prepared for the PREISM workshopERS Washington DC
May 2011
Optimal Management of Established Bioinvasions
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
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
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
Special (Spatial) Modeling Issues
heterogeneity
boundaries
spatial geometry
diffusion process
The model
invadable landinvaded landborder controlclearing
Invasion spread− Cellular automaton model− Approximates reaction-
diffusion Control options
– Spread prevention– Invasion clearing
Min. total costs & damages Simplicity
- 2n*t configurations($d)
($b)
($e)
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
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
2N
5x5 225 33,564,432
Mathematical model
variables parameters
Subject to: damages clearingcosts
spreadprevention
costsCell remains invaded unless cleared
Cell becomes invaded if has invaded neighbor unless prevention applied
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
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
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
Larger delay higher total costs and damages
Total (optimized)
costs & damages
Experiment 1: Initial invasion size
Experiment 2: Landscape size
Finding: Larger landscapes demand greater levels of control
Reason: Larger uninvaded areas Higher potential long-term damages
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
Experiment 4: Invasion location
Central invasions - higher potential long-term damages more control
Invasions near range edge - lower control costs
more control
Central invasions higher costs & damages
Invasion location has ambiguous effect on optimal control effort
t = 0t = 1t = 2t = 3t = 4t = 5t = 6…
Spatial control strategies I:
1) Prevent spread in direction of high potential long-term damages
2) Reduce the extent of invasion edge prior to containment
t = 0t = 1t = 2t = 3t = 4t = 5t = 6…
Spatial control strategies II:1) Reduce the extent of invasion edge2) Protect areas with high potential
damages
t = 0t = 1t = 2t = 3…
Spatial control strategies III:
Again, reduce invasion edge prior to containment.11 7 edges exposed
t = 0t = 1t = 2t = 3t = 4t = 5t = 6…
Spatial control strategies IV:
t = 0t = 1t = 2t = 3t = 4t = 5t = 6t = 7t = 8t = 9
Spatial control strategies V:Protect large uninvaded areas
Entire landscape matters
Barrier cost (b) = 50Removal cost (e) = 1500Baseline damages (d) = 1
No control… let spread
If landscape homogeneous
t = 3t = 4t = 6t = 1t = 5t = 7t = 8
Barrier cost (b) = 50Removal cost (e) = 1500Baseline damages (d) = 1High damages (d) = 101
t = 0t = 2
EradicateIf high damage patch in landscape
t = 3t = 4t = 5t = 6t = 7t = 8
Barrier cost (b) = 50Removal cost (e) = 10000Baseline damages (d) = 1High damages (d) = 101
t = 0t = 1t = 2
Slow spread; protect high damage patchIf higher removal costs
t = 9t = 10t = 11t = 12t = 13t = 14t = 15t = 16t = 17…
t = 3t = 4t = 5t = 6t = 7t = 8
Barrier cost (b) = 50Removal cost (e) = 10000Baseline damages (d) = 1High damages (d) = 51
t = 0t = 1t = 2
Slow the spreadIf lower damages in patch
t = 9t = 10t = 11t = 12t = 13…
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
Modeling multi-manager landscapes
invaded
adjacent to “about to be invaded”
about to be invaded
Offer to “about to beinvaded” cell to induceprevention
•Unilateral management•Bilateral bargaining•Local “club” formation
Border control cost (b)
Outcomes from private control vs. optimal control:
Unilateral management Bilateral bargaining Local “club” coordination
Optimal control
Border control cost (b)
Thank you!!