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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
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
Boiga irregularis
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
*
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)
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*
PV costs + damage if Nc* < Nmin
• If N*c < Nmin, we must then consider the costs of preventing re-entry.
Z =
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
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)
Choose optimal population
If N* Nmin, same as existing invader case
Control only
If N* < Nmin,
Iterative prevention/removal cycle
Case study: Hawaii
Approximately how many snakes currently reside in Hawaii?
Conversations with expert scientists: between 0-100
Growth
Logistic: b=0.6, K=38,850,000
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
Biodiversity Losses
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
Probability of arrival a
function of spending
0.60.2( ) yp y e
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
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
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
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