Integrated Bioeconomic Modeling of
Invasive Species Management
David Finnoff
Jason Shogren
John Tschirhart
University of Wyoming
Chad Settle
University of Tulsa
Brian Leung
McGill University
David Lodge
University of Notre Dame
Michael Roberts
ERS/USDA
August 2004
ERS
• Progress—working toward integrating specific
modeling approaches into one general framework
• Application to leafy spurge
Phase I:
Endogenous Risk
with discounting and risk aversion,
Endogenous Risk
•
Captures risk-benefit tradeoffs
•
Stresses that management priorities depend
crucially on:
The tastes of the manager
— over time and risk bearing
The technology of risk reduction
—prevention, control, and adaptation
•
Managers with different preferences will likely
make different choices on the mix of prevention
and control.
Investigate how changes in a manager’s preferences
over time and over risk affect the optimal strategy
mix:
1.
Explore comparative statics on how changing
tastes affect the technology mix.
2. Implement the model to a specific application of
managing zebra mussels in a lake.
Schematic of the Invasion Process
qH3
IH
IH
(1-qH3)
q2
IL
I
p1
t=0
(1-q2)
(1-p1)
N
t=1
p2
I
(1-p2)
N
t=2
IL
qL3
IH
(1-qL3)
IL
IH
q3
(1-q3)
IL
p3
I
(1-p3)
N
t=3
Dynamic Endogenous Risk
Stage 1:
Stage 2: max
St , X t
P
P
P
ˆ P (.)
max
U
M

D
(
Z
;
N
)

C
(
Z
)

Z


t
t
t
t
t
t
t
t
P
Zt


U t M t  Dt ( ZˆtP ; Nt )  Ct ( St , X t , ZˆtP );   Et W ( Nt 1 ; )

 qt 1 ( X t Nt )U t 1 M t 1  Dt 1 ( ZˆtP1; Nt 1 )  Ct 1 ( St 1 , X t 1 , ZˆtP1 );
EtW ( N t 1 )  pt 1 ( St ) 
  1  q ( X N ) U M  C ( S , X , Zˆ P );
t 1
t
t
t 1
t 1
t 1
t 1
t 1
t 1

 1  p ( S ) U M  C ( S , X , Zˆ P );

t 1
t
t 1

t 1
 
t 1
t 1

t 1
t 1




Comparative Statics – Risk
Aversion
Direct
Effect
Indirect
Effect
S   EMBP  MCP Wxx   EMBC  MCC Wsx


H
Direct
Effect
Indirect
Effec
X   EMBC  MCC Wss   EMBP  MCP Wsx


H
Simulation Results 1
Mean Annual Collective Prevention
Mean Annual Collective Control
0.14
0.6
0.11
0.3
0.08
0.05
0
RN
RA1
RA2
Risk Aversion
RA3
RN
RA1
RA2
Risk Aversion
0%
3%
0%
3%
5%
15%
5%
15%
RA3
Simulation Results 2
Mean Annual Welfare
Mean Annual Probability of Invasion
48
0.5
47.96
0.3
0.1
RN
47.92
RA1
RA2
Risk Aversion
RA3
RN
RA1
RA2
Risk Aversion
0%
3%
0%
3%
5%
15%
5%
15%
RA3
Leafy Spurge Application
Pop growth
Biological
data
Env Factors
Distr area/
population size
Spread
Study
sites
Prevention agency run expense
Prevention cost
Economic
data
Prevention effort expense
Equipment, labor,
employment,
herbicide, etc.
Control agency run expense
Control cost
Damage due to
leafy spurge
Control effort expense
Equipment, labor,
employment,
herbicide, etc.
Direct damage: husbandry
Indirect damage: ecosystems impacts
Conclusions
• Explored how changes in a manager’s preferences
for time and risk-bearing influence optimal strategy
mix
• Impacts are species-specific & rest on whether
direct effects dominate the other through indirect
effects
• less risk averse managers who are far sighted,
invest more in prevention, less in control, and
require less private adaptation
• Reduced risk aversion on the part of the manager
yields lower probabilities of invasion, lower invader
populations, and increased welfare
• Risk aversion induces a manager to want to avoid
risk—both from the invader and from the input used
- go with the safer bet—control
• More exploration into the underlying preferences of
managers may be worthwhile to better understand
how such effects might influence invasives
management
Phase II:
General Equilibrium, Competition,
& the Influence of Fundamental Resources
GEEM
Ri  (eai  e0 ) xi  fi ( xi )  i
dfi ( x)
eai  e0 
 0  xˆi
dxi
m
 Ni ai xi  A  eˆoi
i 1
N
t 1
1 Rˆi  r
 N  N [ ss  1]
s r
t
t



ˆi
R



Temperature
ei  e0
xˆ(ei , e0 , i ) 
2i [(t  ti ) 2  1]
fi ( xi ; t )  i xi 2[(t  ti )2  1]


i
xˆ  

2

[(
t

t
)

1]
 i

i
0.5
eˆ  eai  2  ii  [(t  ti )2  1]0.5
ss
i
0.5
ss
0
e0
b
e01
R1 = 0
e0'
a
t'
t1
t"
t'"
t
Predictions
0.5
2
0.5
2
e

2(


)
[(
t

t
)

1]

e

2(


)
[(
t

t
)
 1]
j
 i
j j
j
i i
i
max SEL
400
350
300
250
200
150
100
50
2
1
4
1
Plant
E(pi)
1
5
2
2
3
6
3
3
-2345 -1111 -2626
4
5
6
temperature
4
5
6
35
115
35
Invasion 1
250
7
Biomass, Plant 1
Biomass, Plant 2
6
200
5
150
4
100
3
2
50
Period
1
Period
0
1
5
9 13 17 21 25 29 33 37 41 45 49
200
0
1
5
9 13 17 21 25 29 33 37 41 45 49
T ~ U(min 0, max 6)
Biomass, Plant 3
150
100
T ~ N(mean 3, st dev 0.75)
50
Period
0
1 5 9 13 17 21 25 29 33 37 41 45 49
Invasion 2
1000
Biomass, Plant 4
800
600
400
200
Period
0
1 5 9 13 17 21 25 29 33 37 41 45 49
1000
800
600
400
200
0
Biomass, Plant 6
Period
1 5 9 13 17 21 25 29 33 37 41 45 49
Biomass, Plant 5 (Invader)
1200
1000
T ~ U(min 0, max 6)
800
600
400
200
0
T ~ N(mean 3, st dev 0.75)
Period
1 5 9 13 17 21 25 29 33 37 41 45 49
Humans
Biomass Harvests
  6  e6h 
xˆ  

2

[(
t

t
)

1]
 6

6
t
0.5
s
6


6
xˆ  
2
cH 
  6[(t  t6 )  1]e 
s
6
e  ea6  2   6  e6h   [(t  t6 )  1]
t 0.5
s
0
Herbicide
0.5
6
2
0.5
0.5
t
eˆ  ea6  2  6  6  [(t  t6 )  1] e
0.5
s
0
2
SEL
P6 no harvests / herbicide
P6 harvests / herbicide
P1
P2
P3
P4
P5
Temperature
tmin
tmax
0.5 0.5( cH t )
Conclusions
•
Theory of plant competition based in individual plant
physiological parameters and maximizing behavior
•
Theory starts prior to the population dynamics and builds on a
behavioral basis
•
Captures redundancy in the plant community
•
Species with max expected valued of SS SEL parabola(s) are
only non-redundant species
•
If invading species is non-redundant – it will dominate
•
Limitations
o Only addresses resource competition
o Omits mutualism & only considers mature plants & lacks
age structure
Phase III:
Optimal Control Model
Optimal Control
• Determines Paths to Steady State
under different scenarios, with:
– no action by ranchers/farmers & land
managers
– action taken only by ranchers/farmers
– action taken by both
• Accounts for the impact of actions
taken by ranchers/farmers
• Flexibility to account for first-best path and
welfare losses under second-best paths
• Allows for economically viable and nonviable harvesting of invasive
• Includes benefits/costs between steady
states instead of simply a comparison of
steady states
Species Equations of Motion


IS  IS ( IS , CR, his , mis )


CR  CR(CR, IS , hcr )
Representative Rancher/Farmer
MaxU (hcr (CR, Tcr ), his ( IS , Tis ); X )
s.t.Tcr  Tis  Tt
Land Manager as a Social Planner
T
Max  U (hcr (CR, Tcr ), his ( IS , Tis ); X )e rt dt
0



s.t. CR, IS , X , mis  mx  mt
Invader Population Across Scenarios
45000
40000
35000
30000
25000
20000
15000
10000
5000
0
No Control
No Land Manager
Control
Optimal Control
Year 0 Year 20 Year 40 Year 60 Year 80
Native Population Across Scenarios
3000000
2500000
No Control
2000000
1500000
No Land Manager
Control
1000000
Optimal Control
500000
0
Year 0 Year 20 Year 40 Year 60 Year 80
Conclusions
• Illustrate how accounting for actions by
ranchers/farmers and feedbacks affect
predictions on species populations
• Show how the various paths to a steady
state are altered by activity/inactivity of
each party
• Explore optimal action by land managers
given model assumptions
Remaining tasks
• Phase IV: Leafy spurge in Thunder Basin
Grasslands
• Phase V: Implications
• Phase VI: “Supermodel” validation