integrated bioeconomic modeling of invasive species management
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Integrated Bioeconomic Modeling of Invasive Species Management
David FinnoffJason ShogrenJohn Tschirhart
University of Wyoming
Chad SettleUniversity of Tulsa
Brian LeungMcGill University
David LodgeUniversity of Notre Dame
Michael RobertsERS/USDA
August 2004ERS
• 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 bearingThe 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
t=0
t=1
N
I
N
N
t=2
t=3
I
I
IH
IH
IH
IH
IL
IL
IL
IL
p1
(1-p1) p2
(1-p2)p3
(1-p3)
q2
qH3
qL3
q3
(1-q2)
(1-q3)
(1-qL3)
(1-qH3)
Dynamic Endogenous RiskStage 1: ˆmax ( ; ) ( ) (.)
Pt
P P P Pt t t t t t t t
ZU M D Z N C Z Z
Stage 2: 1,
ˆ ˆmax ( ; ) ( , , ); ( ; )t
t t
P Pt t t t t t t t t t
S XU M D Z N C S X Z E W N
1 1 1 1 1 1 1 1 1 1
1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
ˆ ˆ( ) ( ; ) ( , , );( ) ( )
ˆ1 ( ) ( , , );
ˆ1 ( ) ( , , );
P Pt t t t t t t t t t t t
t t t t Pt t t t t t t t t
Pt t t t t t t t
q X N U M D Z N C S X ZE W N p S
q X N U M C S X Z
p S U M C S X Z
Comparative Statics – Risk Aversion
Direct Effect Indirect Effect
xx sxEMBP MCP W EMBC MCC WSH
Direct Effect Indirect Effec
ss sxEMBC MCC W EMBP MCP WXH
Simulation Results 1
Risk AversionRN RA1 RA2 RA30
0.3
0.6
0% 3%5% 15%
Mean Annual Collective Prevention
Risk AversionRN RA1 RA2 RA3
0.05
0.08
0.11
0.14
0% 3%5% 15%
Mean Annual Collective Control
Simulation Results 2
Risk AversionRN RA1 RA2 RA3
0.1
0.3
0.5
0% 3%5% 15%
Mean Annual Probability of Invasion
Risk AversionRN RA1 RA2 RA3
47.92
47.96
48
0% 3%5% 15%
Mean Annual Welfare
Leafy Spurge Application
Biological data
Economic data
Study sites
Pop growth
Env Factors Distr area/ population size
Spread
Prevention cost
Control cost
Damage due to leafy spurge
Direct damage: husbandry
Indirect damage: ecosystems impacts
Control agency run expense
Control effort expense Equipment, labor,
employment, herbicide, etc.
Prevention agency run expense
Prevention effort expense Equipment, labor,
employment, herbicide, etc.
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
GEEM0( ) ( )i i i i i iR ea e x f x
0( ) ˆ0i
i iii
df xea e xdx
1ˆ1[ 1]t t t i
ssR rN N N
s r
1ˆ
m
i i i oii
N a x A e
ˆiR
Temperature
0.5
2ˆ[( ) 1]
ss ii
i i
xt t
0.5 2 0.5
0ˆ 2 [( ) 1]ssi i i ie ea t t
2 2( ; ) [( ) 1]i i i i if x t x t t
00 2ˆ( , , )
2 [( ) 1]i
i ii i
e ex e et t
e0
e0'
t
R1 = 0
a
b
t1 t" t' t'"
e01
Predictions
1 2 3 4 5 6temperature
50100150200250300350400max SEL
1
2
5
4 36
0.5 2 0.5 22( ) [( ) 1] 2( ) [( ) 1]j j j j i i i ie t t e t t
Plant 1 2 3 4 5 6E(pi) -2345 -1111 -2626 35 115 35
0
50
100
150
200
250
1 5 9 13 17 21 25 29 33 37 41 45 49
Period
Invasion 1
Biomass, Plant 1
0
1
2
3
4
5
6
7
1 5 9 13 17 21 25 29 33 37 41 45 49
Period
0
50
100
150
200
1 5 9 13 17 21 25 29 33 37 41 45 49
Period
T ~ U(min 0, max 6)
T ~ N(mean 3, st dev 0.75)
Biomass, Plant 2
Biomass, Plant 3
Invasion 2
T ~ U(min 0, max 6)
T ~ N(mean 3, st dev 0.75)
0
200
400
600
800
1000
1 5 9 13 17 21 25 29 33 37 41 45 49
Period
Biomass, Plant 4
0200400600800
1000
1 5 9 13 17 21 25 29 33 37 41 45 49
Period
Biomass, Plant 6
0200400600800
10001200
1 5 9 13 17 21 25 29 33 37 41 45 49
Period
Biomass, Plant 5 (Invader)
Humans
0.5
6 66 2
6 6
0.5 0.5 2 0.50 6 6 6 6 6
ˆ[( ) 1]
2 [( ) 1]
ts
s t
e hxt t
e ea e h t t
0.5
66 2
6 6
0.5 2 0.5 0.5( )0 6 6 6 6
ˆ[( ) 1]
ˆ 2 [( ) 1]
t
t
scH
s cH
xt t e
e ea t t e
P6 harvests / herbicide
SEL
Temperature
tmin tmax
P1
P2
P3
P4
P5
P6 no harvests / herbicide
Biomass Harvests
Herbicide
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
• Limitationso Only addresses resource competitiono 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 non-viable harvesting of invasive
• Includes benefits/costs between steady states instead of simply a comparison of steady states
Species Equations of Motion
),,(
),,,(
cr
isis
hISCRCRCR
mhCRISISIS
Representative Rancher/Farmer
tiscr
isiscrcr
TTTtsXTIShTCRhMaxU
..));,(),,((
Land Manager as a Social Planner
T
rtisiscrcr dteXTIShTCRhUMax
0
));,(),,((
txis mmmXISCRts
,,,..
Invader Population Across Scenarios
05000
1000015000200002500030000350004000045000
Year 0 Year 20 Year 40 Year 60 Year 80
No Control
No Land ManagerControl
Optimal Control
Native Population Across Scenarios
0
500000
1000000
1500000
2000000
2500000
3000000
Year 0 Year 20 Year 40 Year 60 Year 80
No Control
No Land ManagerControl
Optimal Control
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
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