Control of Invasive Control of Invasive Species: Species: Lessons from Miconia Lessons from Miconia in Hawaiiin Hawaii

Kimberly Burnett, Brooks Kaiser, Kimberly Burnett, Brooks Kaiser, Basharat A. Pitafi, James RoumassetBasharat A. Pitafi, James Roumasset

University of Hawaii, Manoa, HIUniversity of Hawaii, Manoa, HIGettysburg College, Gettysburg, PAGettysburg College, Gettysburg, PA

ObjectivesObjectives

Inform public policy decisions for invasive Inform public policy decisions for invasive species using economic theory:species using economic theory: Optimal control of an existing invaderOptimal control of an existing invader

Case study from Hawaii…Case study from Hawaii…

Our caseOur case

Existing invader:Miconia calvescens

Minimize NPV Minimize NPV (Costs+damages)(Costs+damages)

NPV of NPV of reducingreducing population to population to N N consists of:consists of:

1. Transition cost of reducing the population from1. Transition cost of reducing the population from

toto

2. 2. Cost of maintaining population Cost of maintaining population atat

3. 3. Damages incurred from remaining at Damages incurred from remaining at

0

0

( ) ( ) ( )Total cost ( ) ( )

Nc N g N D N

V N N c N dNr r

N

0NN

NN

NPV of NPV of increasingincreasing population to population to N N consists of:consists of:::

1. 1. Transition damage associated with this time Transition damage associated with this time and pop’n leveland pop’n level

2. 2. Cost of maintaining population Cost of maintaining population atat

3. 3. Damages incurred from remaining at Damages incurred from remaining at

0

0( ) ( ) ( )

Total cost ( ) ( )rt

tc N g N D N

V N N D N dter r

t

NN

Minimize NPV Minimize NPV (Costs+damages)(Costs+damages)

N

An Algorithm for An Algorithm for Minimizing Costs + Minimizing Costs + DamagesDamages

( ) 0, ( ) 0, ( ) 0, ( ) 0t t t tc N c N D N g N

0

0

0

0

0

( ) ( ) ( )( ) , 0

V( , )( ) ( ) ( )

( ) , MAX

N

n

T

rtt

t

c N g N D Nc N dN N n

r rNn

c N g N D ND dt N Ne n n

r r

Existing invader: Existing invader: methodologymethodology

Choosing Choosing Min[V(nMin[V(n00,N)],N)] determines optimal steady determines optimal steady

state population level state population level N*, corresponding to N*, corresponding to NN0.0.

N*N* minimizes costs and damages over time and:minimizes costs and damages over time and:

may be smaller (including zero) than the existing may be smaller (including zero) than the existing populationpopulation

or larger (including carrying capacity) than the existing or larger (including carrying capacity) than the existing populationpopulation

Is potentially dependent on the current invasion level Is potentially dependent on the current invasion level

Case StudyCase Study

Growth function g(N)Growth function g(N) Damage function D(N)Damage function D(N) Control cost function C(N,x)Control cost function C(N,x)

Miconia: GrowthMiconia: Growth

b, intrinsic growth rate: 0.3 b, intrinsic growth rate: 0.3 from analysis of the spread of the tree on from analysis of the spread of the tree on

Hawaii since 1960s introductionHawaii since 1960s introduction

K, carrying capacity: 100,000,000 K, carrying capacity: 100,000,000 (100 trees per acre over 1 million acres above (100 trees per acre over 1 million acres above

the 1800 mm/yr rainfall line)the 1800 mm/yr rainfall line)

( ) 1 ,n

g n bnK

Miconia: DamagesMiconia: Damages Endangered birdsEndangered birds

Households willing to pay $31/ bird species /year to keep a species Households willing to pay $31/ bird species /year to keep a species from extinction (Loomis and White 1996) from extinction (Loomis and White 1996)

Full threat of loss in biodiversity on all islands equivalent to a loss of Full threat of loss in biodiversity on all islands equivalent to a loss of ½ the endangered bird species ½ the endangered bird species →→ $103-303 mill / year $103-303 mill / year

WatershedWatershed Groundwater recharge losses Groundwater recharge losses →→ $137 million /year (Kaiser and $137 million /year (Kaiser and

Roumasset 2002) Roumasset 2002) Increased sedimentation Increased sedimentation → → $33.9 million /year (Kaiser and $33.9 million /year (Kaiser and

Roumasset 2000) Roumasset 2000)

Total damagesTotal damages Estimated average of $377.4 million per year Estimated average of $377.4 million per year If any 1 tree equally responsible for its portion of damages, per-tree If any 1 tree equally responsible for its portion of damages, per-tree

damage rate of $3.77 damage rate of $3.77 ( ) 3.77D n n

Biodiversity

Ecosystem services

Miconia: Control costMiconia: Control cost

““Search” component Search” component ““Treatment” component Treatment” component 2003: total number of trees controlled on 4 islands: 2003: total number of trees controlled on 4 islands:

72,339 72,339 Annual control expenditures $1 million Annual control expenditures $1 million 72,339 trees removed thought to be less than ¼ of 72,339 trees removed thought to be less than ¼ of

existing population existing population

1.66

1,000,000,000( , ) 13.39 *C n x x

n

Miconia: Results Miconia: Results (High damages)(High damages)

Current stock: 400,000Current stock: 400,000 << Reduce stock to N* = 31,295 trees, maintainReduce stock to N* = 31,295 trees, maintain

*N 0N

PV losses for N0 = 400,000

0 31,295 400,000 100 m N (Stationary)

D(N)=$2.74N -> 34,202 treesD(N)=$4.88N-> 28,803 trees

If lower damages, If lower damages, Global min at N*=31,295, Global min at N*=31,295, Local min at N*=100 mLocal min at N*=100 m

Illustrates need to check both above and below initial Illustrates need to check both above and below initial populationpopulation

Miconia: ResultsMiconia: Results(Low Damages)(Low Damages)

PV losses for N0

0 2.8 k 400 k 4.4 m 100 m N (stationary)

Miconia policy: status quo vs. Miconia policy: status quo vs. optimal (win-win)optimal (win-win)

 

First period

removal cost

Annual removal

costPV costs

Annual damages

NPV damages

PV (losses)

Status quo

$1 m $1 m $50 m $369.5 m $12.35 b -$12.4 b

Optpolicy

$6.27 m $449,245 $28.7 m $117,982 $7.4 m -$36.1 m

SummarySummary

Status quo policy welfare equivalent of doing nothingStatus quo policy welfare equivalent of doing nothing Optimal control of invasive species requires integrated Optimal control of invasive species requires integrated

assessment of bio-economic threatassessment of bio-economic threat Growth pattern, control costs, and damages must be Growth pattern, control costs, and damages must be

estimated as functions of population and removalestimated as functions of population and removal Optimal policies dependent on initial population at time Optimal policies dependent on initial population at time

of actionof action Eradication, internal steady state, accommodation all viable Eradication, internal steady state, accommodation all viable

outcomesoutcomes Catastrophic damages from continuation of status quo Catastrophic damages from continuation of status quo

policies can be avoided at costs even lower than policies can be avoided at costs even lower than current spending trajectorycurrent spending trajectory

Limitations and direction Limitations and direction for further researchfor further research

Overall:Overall: Sophistication of growth, control cost Sophistication of growth, control cost

functionsfunctions Accurate anticipation of damages, Accurate anticipation of damages,

particularly ecologicalparticularly ecological Seed bank, spatial dimensions improvedSeed bank, spatial dimensions improved