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