Integrating Prevention and Control of Invasive Species: The Case of the Brown Treesnake
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Transcript of Integrating Prevention and Control of Invasive Species: The Case of the Brown Treesnake
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Integrating Prevention and Control of Invasive Species: The Case of the
Brown TreesnakeKimberly Burnett, Brooks Kaiser,
Basharat A. Pitafi, James Roumasset
University of Hawaii, Manoa, HIGettysburg College, Gettysburg, PA
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Objectives
Illustrate dynamic policy options for a highly likely invader that has not established in Hawaii
Find optimal mix of prevention and control activities to minimize expected impact from snake
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Boiga irregularis
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Methodology
First consider optimal control given N0 (minimized PV of costs and damages) =>Nc
*
We define prevention to be necessary if the population falls below Nmin (i.e., Nc
* < Nmin)
Determine optimal prevention expenditures (to decrease probability of arrival) conditional on the minimized PV from Nc
*
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Nc*
Nmin Nc*
< Nmin
We have a winner!
N* = Nc*
N0 ≥ Nmin
V(Nmin)
Choose y to min cost of removal/prevention cycle
Nc* = Best stationary N without prevention
Z(Nc*)
N* = Min (Z,V)
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Algorithm to minimize cost + damage
0
0
0
0
0
( ) ( ) ( )( ) , 0
V( , )( ) ( ) ( )
( ) , ( ), MAX
N
n
Trt
t
t
c N g N D Nc N dN N n
r rNn
c N g N D ND dt n g n N Ne n n
r r
0Min V( , )N
Nn => V* => Nc*
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PV costs + damage if Nc* < Nmin
• If N*c < Nmin, we must then consider the costs of preventing re-entry.
Z =
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Prevention/eradication cycle
Expected present value of prevention and eradication:
p(y): probability of successful introduction with prevention expenditures y. Minimizing Z wrt y results in the following condition for optimal spending y:
11
( ) 1 (1 ) ( ) =
11t
t
y p y E r y p y EZ y
r rr
( )1
(1 )
p y E
r
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Nc*
Nmin Nc*
< Nmin
We have a winner!
N* = Nc*
N0 ≥ Nmin
V(Nmin)
Choose y to min cost of removal/prevention cycle
Nc* = Best stationary N without prevention
Z(Nc*)
N* = Min (Z,V)
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Choose optimal population
If N* Nmin, same as existing invader case
Control only
If N* < Nmin,
Iterative prevention/removal cycle
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Case study: Hawaii
Approximately how many snakes currently reside in Hawaii?
Conversations with expert scientists: between 0-100
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Growth
Logistic: b=0.6, K=38,850,000
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Damage
Power outage costs: $121.11 /snake
Snakebite costs: $0.07 /snake
Biodiversity: $0.32 – $1.93 /snake
Total expected damages:
122.31 tD n
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Biodiversity Losses
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Control cost
Catching 1 out of 1: $1 million
Catching 1 out of 28: $76,000
Catching 1 out of 39m: $7
0.621
378,512( )c n
n
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Probability of arrival a
function of spending
0.60.2( ) yp y e
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ResultsAside from prevention, eradicate to zero and stay there.Since prevention is costly, reduce population from 28 to 1 and maintain at 1
5 10 15 20 25 30
-5 107
-4 107
-3 107
-2 107
-1 107
$ PV
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Snake policy: status quo vs. optimal (win-win)
First period cost
Annual cost
PV costs
Annual damage
s
NPV damage
s
PV losses
Status quo
$2.676 m $2.676 m $133.8 m $4.5 b $145.9 b $146.1 b
Opt.policy $2.532 m $227,107 $13.88 m $121 $9,400 $13.89 m
NPV of no further action: $147.3 billion
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SummaryRe-allocation between prevention and control may play large role in approaching optimal policy even at low populations
Eradication costs increased by need for prevention, which must be considered a priori
Catastrophic damages from continuation of status quo policies can be avoided at costs much lower than current spending trajectory
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Uncertainties
1. Range of snakes currently present (0-100?)• 8 captured
• More may’ve gotten away
• Not much effort looking
2. Probability of reproduction given any pop’n level• Don’t know, need to look at range of possibilities
• Here all control
• If N*<Nmin, prevention makes sense
• Need to find optimal mix