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