Transcript Integrating Prevention and Control of Invasive Species: Lessons

Control of Invasive
Species:
Lessons from Miconia
in Hawaii
Kimberly Burnett, Brooks Kaiser,
Basharat A. Pitafi, James Roumasset
University of Hawaii, Manoa, HI
Gettysburg College, Gettysburg, PA
Objectives
 Inform public policy decisions for invasive
species using economic theory:
 Optimal control of an existing invader
 Case study from Hawaii…
Our case
Existing invader:
Miconia calvescens
Minimize NPV (Costs+damages)
NPV of reducing population to N
consists of:
1. Transition cost of reducing the population from N 0
to N
2. Cost of maintaining population at N
3. Damages incurred from remaining at N
N
Total cost  V ( N 0  N ) 

N0
c( N ) g ( N ) D ( N )
c( N )dN 

r
r
Minimize NPV (Costs+damages)
NPV of increasing population to N
consists of::
1. Transition damage associated with this time
and pop’n level N
2. Cost of maintaining population at N
3. Damages incurred from remaining at N
t

c( N ) g ( N ) D( N )
Total cost  V ( N 0  N )   e D( N )dt 

r
r
t0
 rt
An Algorithm for Minimizing
Costs + Damages
N
c( N ) g ( N ) D ( N )
 c( N )dN 

,
0  N  n0
r
r

n0
V( n 0, N )  
T

c( N ) g ( N ) D ( N )
 rt

, n 0  N  N MAX
  e D ( n t )dt 
r
r
 t 0


c( Nt )  0, c( Nt )  0, D( N t )  0, g ( N t )  0
Existing invader:
methodology
 Choosing Min[V(n0,N)] determines optimal
steady state population level N*, corresponding
to N0.
 N* minimizes costs and damages over time and:
 may be smaller (including zero) than the existing
population
 or larger (including carrying capacity) than the existing
population
 Is potentially dependent on the current invasion level
Case Study
 Growth function g(N)
 Damage function D(N)
 Control cost function C(N,x)
Miconia: Growth
n

g ( n )  bn  1   ,
K

 b, intrinsic growth rate: 0.3
 from analysis of the spread of the tree on
Hawaii since 1960s introduction
 K, carrying capacity: 100,000,000
 (100 trees per acre over 1 million acres
above the 1800 mm/yr rainfall line)
Miconia: Damages
 Endangered birds
 Households willing to pay $31/ bird species /year to keep a species
from extinction (Loomis and White 1996)
 Full threat of loss in biodiversity on all islands equivalent to a loss of
½ the endangered bird species → $103-303 mill / year
 Watershed
 Groundwater recharge losses → $137 million /year (Kaiser and
Roumasset 2002)
 Increased sedimentation → $33.9 million /year (Kaiser and
Roumasset 2000)
 Total damages
 Estimated average of $377.4 million per year
 If any 1 tree equally responsible for its portion of damages, per-tree
damage rate of $3.77
D ( n )  3.77n
Biodiversity
Ecosystem services
Miconia: Control cost
1, 000, 000, 000 

C (n, x)  13.39 
* x
1.66
n


 “Search” component
 “Treatment” component
 2003: total number of trees controlled on 4 islands:
72,339
 Annual control expenditures $1 million
 72,339 trees removed thought to be less than ¼ of
existing population
Miconia: Results
(High damages)
 Current stock: 400,000
 N * < N0
 Reduce stock to N* = 31,295 trees, maintain
PV losses for N0 = 400,000
D(N)=$2.74N -> 34,202 trees
D(N)=$4.88N-> 28,803 trees
0 31,295
400,000
100 m
N (Stationary)
Miconia: Results
(Low Damages)
 If lower damages,
 Global min at N*=31,295,
 Local min at N*=100 m
PV losses for N0
0 2.8 k
400 k
4.4 m
100 m
N (stationary)
 Illustrates need to check both above and below initial
population
Miconia policy: status quo vs.
optimal (win-win)
First
period
removal
cost
Annual
removal
cost
PV costs
Annual
damages
NPV
damages
PV
(losses)
Status
quo
$1 m
$1 m
$50 m
$369.5 m
$12.35 b
-$12.4 b
Opt
policy
$6.27 m
$449,245
$28.7 m
$117,982
$7.4 m
-$36.1 m
Summary
 Status quo policy welfare equivalent of doing nothing
 Optimal control of invasive species requires integrated
assessment of bio-economic threat
 Growth pattern, control costs, and damages must be estimated
as functions of population and removal
 Optimal policies dependent on initial population at time
of action
 Eradication, internal steady state, accommodation all viable
outcomes
 Catastrophic damages from continuation of status quo
policies can be avoided at costs even lower than
current spending trajectory
Limitations and direction
for further research
 Overall:
 Sophistication of growth, control cost
functions
 Accurate anticipation of damages,
particularly ecological
 Seed bank, spatial dimensions improved