Front Cover
 Center information
 Will zebra mussels invade...
 Lake Okeechobee
 Zebra mussel model
 Empirical model parameters
 Four management scenarios
 Breakpoint parameter values

Group Title: Policy Brief Series - International Agricultural Trade and Policy Center. University of Florida ; no. 07-03
Title: An economic model for evaluating zebra mussel management strategies
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00089783/00001
 Material Information
Title: An economic model for evaluating zebra mussel management strategies
Series Title: Policy Brief Series - International Agricultural Trade and Policy Center. University of Florida ; no. 07-03
Physical Description: Book
Language: English
Creator: Lee, Donna J.
Adams, Damian C.
Publisher: International Agricultural Trade and Policy Center, Institute of Food and Agricultural Sciences, University of Florida
Institute of Food and Agricultural Sciences, University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007
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Bibliographic ID: UF00089783
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.


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Table of Contents
    Front Cover
        Page i
    Center information
        Page ii
        Page 1
        Page 2
    Will zebra mussels invade Florida?
        Page 3
    Lake Okeechobee
        Page 4
    Zebra mussel model
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
    Empirical model parameters
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
    Four management scenarios
        Page 16
        Page 17
        Page 18
        Page 19
    Breakpoint parameter values
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
Full Text

PBTC 07-03

I ional Agricultural Trade and Policy Center



Institute of Food and Agricultural Sciences

An Economic Model for Evaluating
Zebra Mussel Management Strategies
Donna J. Lee and Damian C. Adams *

PBTC 07-03 July 2007



The International Agricultural Trade and Policy Center (IATPC) was established in 1990
in the Institute of Food and Agriculture Sciences (IFAS) at the University of Florida
(UF). The mission of the Center is to conduct a multi-disciplinary research, education and
outreach program with a major focus on issues that influence competitiveness of specialty
crop agriculture in support of consumers, industry, resource owners and policy makers.
The Center facilitates collaborative research, education and outreach programs across
colleges of the university, with other universities and with state, national and
international organizations. The Center's objectives are to:

* Serve as the University-wide focal point for research on international trade,
domestic and foreign legal and policy issues influencing specialty crop agriculture.
* Support initiatives that enable a better understanding of state, U.S. and international
policy issues impacting the competitiveness of specialty crops locally, nationally,
and internationally.
* Serve as a nation-wide resource for research on public policy issues concerning
specialty crops.
* Disseminate research results to, and interact with, policymakers; research, business,
industry, and resource groups; and state, federal, and international agencies to
facilitate the policy debate on specialty crop issues.

An Economic Model for Evaluating Zebra Mussel Management Strategies


Zebra mussels present an imminent threat to the water resources in Lake Okeechobee in Florida.

The lake is vitally important to consumptive water uses and recreational anglers and provides a

host of ecosystem services. We employ a probabilistic bio-economic simulation model to

estimate the potential impact of zebra mussels to wetland ecosystem services, consumptive water

users, and recreational anglers under alternative public management scenarios. Without public

management, the expected net economic impact from zebra mussels is -$244.1 million over 20

years. Public investment in prevention and eradication will yield a net expected gain of +$188.7

million, a superior strategy to either prevention or eradication alone.

Key Words: Invasive species, cost transfer, surface water, fishing, wetlands, probability

transition matrix

JEL Classifications: C63, Q25, Q52, Q57, Q58

* This document was prepared while the authors were employed as an Associate Professor and a Lecturer in the
Department of Food and Resource Economics in the Institute of Food and Agricultural Sciences, College of
Agriculture and Life Sciences at the University of Florida. For inquiries, contact DLee@Entrix.com.

Donna J. Lee and Damian C. Adams*

An Economic Model for Evaluating Zebra Mussel Management Strategies
Donna J. Lee and Damian C. Adams

Zebra mussels (Dreissena polymorpha) are a small freshwater species native to

Southeastern Europe. In suitable water, zebra mussels become successful invaders. Mature

females can produce up to one million eggs per year (USCACE, 2003). The zebra mussel most

likely crossed the Atlantic Ocean as larvae on a transatlantic ship (Hebert et al., 1989; Griffiths et

al., 1991; Thorp et al., 2002) and disembarked into the Great Lakes. The mussels multiplied

rapidly and began spreading. Today populations are found in twenty-four states as shown in the

map in Figure 1 (USGS, 2007).

Zebra and Ouaqga Mussel Sightings Distribulton

Figure 1. Zebra mussels in the United States (USGS 2007)

The problem with zebra mussels is that they colonize on any submerged surface including

boat hulls, navigational buoys, bridge abutments, and water intake pipes. Their dense mats will

accelerate the rate of corrosion, sink navigational buoys with their weight, and obstruct water

flow in pipes. United States' expenditure for the upkeep required to maintain boat bottoms,
flow in pipes. United States' expenditure for the upkeep required to maintain boat bottoms,

docks pilings, locks, gates, and pipes is estimated to be $60 million per year (USGAO, 2002).

Because zebra mussels are spreading, damages are expected to rise. Future damages are

estimated to be between $3.1 and $5 billion for the period 2002 to 2011 (USGAO, 2002 and

USGS, 2000).

Zebra mussels compete with native flora and fauna for food and space, alter the

composition of the water column, and transform lake bottoms. They will bio-foul rocks, logs,

submerged plants, and the shells of other mussels. In the U.S. more than half of all native

freshwater mussel species are either threatened or endangered. Recovery efforts are significantly

hindered by the presence of zebra mussels (Ricciardi et. al.,1998; USGAO, 2002)

Will Zebra Mussels Invade Florida?

Zebra mussels were first sighted in Florida in 1998 during an inspection of a bait and

tackle shop (University of Florida, 1998). Fortunately a fast acting official collected and

destroyed the animals before they could spread. No other sightings have occurred since, but in

the last decade zebra mussels have made their way south creeping ever closer to the Florida

border. Populations are thriving in Arkansas, Alabama, Kentucky, Louisiana, Mississippi,

Missouri, Tennessee, and West Virginia (USGS, 2007). According to estimates by Drake and

Bossenbroek (2004) zebra mussels are bound to reappear in Florida. The authors estimate that in

the coming years there is a "high" likelihood that zebra mussels will reach north Florida and a

"moderate" likelihood that zebra mussels will reach south Florida. Suitability of Florida's warm

waters was examined by Hayward and Estevez (1997). They judged the rivers in the Florida

panhandle (north Florida) to be unsuitable for zebra mussel propagation because the water is

acidic and contains few minerals. The St. Johns river in north central Florida and Lake

Okeechobee in south Florida both have low acidity and high mineral content and are judged

suitable for sustaining zebra mussels.

This study examines the potential for Lake Okeechobee to become infested with zebra

mussels, describes a simulation model, proffers a series of management scenarios, presents

results, and offers sensitivity tests on key model parameters. Novel contributions include

quantification of potential future damages from zebra mussels, economic trade-offs between

public management expenditures and public and private gains, and comparisons of management

alternatives prevention and eradication.

Lake Okeechobee

Lake Okeechobee is an important commercial shipping route, a valuable source of

freshwater, a major recreational resource, and at 448,000 acres, the second largest lake wholly

contained in the United States, (FDEP, 2001). Five counties around the lake pump water for

irrigation, industry, and household uses. Impacted services from an infestation of zebra mussels

would include water supply, water recreation, and wetland ecosystem services.

The Lake Okeechobee waterway is presently free of zebra mussels and the nearest

populations are 750 miles away. Most likely zebra mussels will make the journey by clinging to

the stems of aquatic weeds entwined in a boat propeller or snagged on a trailer. While the

possibility may seem remote, it is worth noting that zebra mussels can survive several days out

of water. In the Great Lakes region, aquatic weeds covered with live zebra mussels were

observed on 1 out of every 275 boats in parking lots while owners were preparing to launch into

non-infested lakes (Johnson and Carlton, 1996).

Lake Okeechobee is a popular destination for local and out-of-state sport fishers,

recreational boaters, and host to several major fishing tournaments each year. Out-of-state

boaters and returning Florida boaters are likely vectors for transporting zebra mussels to Lake


Zebra mussel model

In a previous work, Leung, et al. (2002) used stochastic dynamic programming to model

the probability of a zebra mussel invasion as a decreasing function of prevention effort. Zebra

mussel growth was captured with a logistic function. Damages were expressed in terms of lost

productivity due to reduced water flow. The optimal solution was to reduce the probability of

arrival by 10% using prevention measures. Finnoff et al. (2005) applied a stochastic dynamic

programming model following Leung et al. (2002) to examine the economics of preventing zebra

mussel damages in a Midwest lake. They questioned the importance of including feedback links

and the conditions under which omission would make a difference. One interesting finding was

that over investment or under investment in control could result depending on how the public

manager believes the private entity will respond to the invasion. To compare management

alternatives for eradicating the oyster drill (Ocinebrellus inornatus) an invasive marine mollusk,

Buhle et al. (2005) employed a Markov approach. The authors specified a 2x2 transition matrix

to capture two of the animals' three life stages and ascertained that control efforts targeting the

adult animals would be more cost effective than control efforts targeting the bright egg masses.

For Lake Okeechobee, we assume there is a real threat of zebra mussel introduction. Once

introduced, the small critters are unlikely to be noticed until dense mats are formed or piles of

razor sharp mussel shells wash up on shore. By the time they are noticed, the economic and

environmental damage will already be significant. To characterize this system we use a stylized

model comprising the following four "states of nature": (1) none, (2) introduced, (3) propagating,

and (4) critical mass. The probability that the Lake will be in any of the four states at time t in the

future, is st. At present, there are no zebra mussels so slto = 1 and it follows that s2to = ssto =

S4t=0 = 0. Some additional description of the variable st appears in Table 1.

Table 1. Description of Zebra Mussel States in Lake Okeechobee

Probability of state i Economic and
i Description of state i
at time t ecosystem damages?

1 sit No zebra mussels no

2 S2t Zebra mussels recently introduced no

3 S3t Zebra mussels propagating no

4 S4t Zebra mussels at critical mass yes

The st state probabilities are brought together to form the elements of vector variable St :

S1 4
S2 4
(1) St = 2 where 0 < s, <1 and Cs, =1 .
S3 i=l
4 _t

At present the Lake has no zebra mussels, so at t = 0,

(2) So= ,

-0 t=0

To derive future state values St+l we define the transition probability a,, which represents the

probability of changing to state i from state j in a single time period. In matrix form, a,j comprise

the elements of Ao the 4x4 matrix of transition probabilities under a natural progression of zebra


a11 a12 a13 a14

(3) A a21 a22 a23 a24
(3) A0=
a31 a32 a33 34
a41 a42 a43 a44

St+l is defined as the product ofAo and St from equations (3) and (1):

(4) St+ =AoSt.

Each element of St+ can be obtained:

(5) s,t+1 = alSlt +a12s2t a3S3t +a4s4t fori =1...4 .

Because the natural progression of zebra mussels may be undesirable, prevention measures

are available to reduce the probability of introduction and propagation. Letting fi measure the

effectiveness of a prevention program, the transition probability matrix Ap with a prevention

program in place is expressed:

all-a21fl a12 a13 a14
(6) A a21 (-l) a22 a23 a24
a31 a32 a33 a34
a41 a42 a43 a44

Propagation can be thwarted with early eradication which is defined as the action required

to destroy all zebra mussels as soon as they are detected. With monitoring as a component of the

prevention program, we assume early eradication takes place in state 3 before the zebra mussels

can cause significant damage or loss. The transition probability matrix Am is represented by:

a11 -2lfl 1 1 1
(7) Am a2(1 l) a22 a 23 a 24
(7) Am ~
a31 0 a33 a34
a41 a42 0 0

Without a prevention program in place, we assume there would be no monitoring and

therefore zebra mussels would be detected with the onset of economic damages, i.e. in state 4.

Late eradication is defined to be the measures taken to destroy all zebra mussels in Lake

Okeechobee after reaching state 4. The transition probability matrix Ar is expressed:

all 1 1 1

(8) A= a21 a22 a23 a24
a31 0 a33 a34
a41 a42 0

Post-eradication, we assume the treated lake would be free of zebra mussels for a period of

at n years during time which the transition probability matrix becomes,



With prevention, the zebra mussel state equation during states pre-introduction (state 1)

and introduction (state 2) is defined:

(10) St A St, .

After zebra mussels are established, prevention measures would no longer be practical,

thus prevention measures would be halted. During propagation (state 3) and critical mass (state

4), the transition matrix is Ao and the state equation reverts back to equation (4).

With prevention and early eradication, the state equation from pre introduction through

introduction, propagation, and early eradication is:

(11) St Am St,

With late eradication, the state equation from pre-introduction through introduction,

propagation, critical mass, and eradication is:

(12) St Ar St_

For the remainder of the planning horizon after early eradication or late eradication the state

equation is:

(13) St =AnSt-l

Economic comparison of the management choices requires estimates of the expected

benefits and costs. For this problem, the management choice variable X is a (4x4) vector

composed of the elements x, and x,.

x, x, 0 0
0 0 0 0
(14) X=
0 0 x, O0
0 0 0 xT

The decision to invest in prevention is given by xp=l and x,=0. The decision to invest in

prevention and early eradication is given by xp=l and x,=l. The decision to invest in late

eradication is given by xp=0 and x,=l. The four management alternatives are shown in Table 2

Table 2. Four management alternatives

p =0 p =1

1 11

x, = 0 Do nothing Invest in prevention

(status quo) (prevention)

Invest in prevention and eradicate
Eradicate when zebra mussels become
x, =1 before zebra mussels become
(late eradication)
(prevention and early eradication)

Combining the two management choices yields a vector of four management alternatives:

(1 xp)(1- x,)

x, (1- x.)
(15) u(X)=
x(1- xP)x

The unit costs of implementing the management choices x, and x, are c, and c, which

comprise the (2x1) management cost vector q.


(16) q=

The cost of management Ct at time t is the product of unit cost q, management choice X, and

the zebra mussel state St from equations (16), (14) and (1):

(17) C,= q'XS,.

Economic damage from zebra mussel infestation is d an X dependent variable of increased

maintenance expenditure by consumptive water users in Lake Okeechobee. Ecosystem service

loss with zebra mussel infestation e includes diminished wetland functions, loss in wildlife

habitat, and reduced aquatic food supply in state 4. The benefit from zebra mussel infestation b is

the added value to recreational and sport fishers from the improved water clarity and increased

catch rate due to zebra mussel filter feeding. In this model, cost, damage, and loss are expressed

as negative values and benefit is expressed as a positive value. The objective is to choose a

management strategy X that maximizes Z the present value of total expected cost, damage, loss,

and benefit with the threat of zebra mussel infestation. The objective is to:

(18) max Z= (1+r)-t(q'XS,)+(e'+b')S, +u(X)'d(X)'S) ,

subject to equations (1) through (17). In (18), r is the annual discount rate and Tis the number of

years in the planning horizon.

Empirical model parameters

Transition probabilities

Recreational and sport boats are the primary vector for transporting zebra mussels from

infested lakes to Lake Okeechobee. We examined data from three national tournaments on Lake

Okeechobee during 2006-2007 (Carson, 2007 and Eads, 2007) and observed that half the 926

anglers were from states with zebra mussel infested waters. The potential for trailered boats to

vector zebra mussels was shown by Bossenbroek et al. (2001). They estimated that trailered

boats in the Great Lakes area could convey enough live zebra mussels to colonize an uninfested

body of water in a nearby state with a probability of between 1.18x10-5 and 4.11x10-5. We used

an intermediate probability of 3.78x10-5 per boat, multiplied by 926 boats per year to obtain an

annual probability of zebra mussel introduction of 3.5% per year (a21 = 0.035)

Upon introduction to Lake Okeechobee, zebra mussels would prosper according to

Hayward and Estevez (1997). The scientists computed habitat suitability indices (HSI) of 0.83

and 0.91 for open water and shallow water containing dense aquatic plants. Given the high HSI

values for Lake Okeechobee and the large expanse of suitable habitat, we assumed introduced

zebra mussels would become established and propagate until critical mass was reached with a

probability of 100% (a2 43 = a44 =1.0). 1

1 These values were chosen to enhance the transparency of the empirical model. Simulations assuming a32 a43= a44
= 0.83 and a32 a43= a44 = 0.91 were also conducted. Results from those runs appear in the appendix in Table 6 and
Table 7.

Time to reach carrying capacity according to Nalepa et al., (1995), Strayer et al. (1996),

Burlakova, Karatayev, and Padilla (2006), Borcherding and Sturm (2002), and Lauer and Spacie

(2004) is two to three years after detection. For our model, we assume zebra mussels will grow

to produce dense mats sufficient to cause damages two years after introduction, thus the time lag

between states 2 and 3, and between states 3 and 4 is one year.

Private economic damage

In the Great Lakes area, O'Neill (1996) and Deng (1996) estimated annual expenditure for

chemical, mechanical and thermal maintenance. For a zebra mussel infestation in Lake

Okeechobee, we assume water users would employ mechanical and thermal means to clear

clogged intake pipes and spend $4.90 per million gallons pumped as reported by Deng (1996).

Mean water withdrawal from Lake Okeechobee is 562,589 million gallons per year (USGS,

2006). Multiplying annual water use by average unit expenditure we arrived at economic

damages of $2.76 million per year to consumptive water users (d2 = 2.76). As most pipes in the

Great Lake region are pre-treated with antifouling paint, we apply this damage estimate to

treated pipes.

Anti-fouling paint helps to reduce maintenance expenditures by inhibiting zebra mussel

colonization. In the Columbia River Basin, water users applied anti-fouling paint to interior pipe

surfaces at a cost of $25.56 per square foot (Phillips, 2005). Based on a survey of Lake

Okeechobee water users (Adams, 2007) we calculated the average interior surface area of intake

pipes to be 300.58 square feet. With 504 major water users on the Lake, we calculate an intake

pipe surface area of 151,492 square feet, which would require $3.87 million to treat with

antifouling paint. Assuming the paint treatment lasts 10 years, annualized mitigation damage is

$0.387 million (d3 = 0.387).

We assume anti-fouling paint treatment saves consumptive uses about 22% in maintenance

expenditures. Thus without treatment, Lake Okeechobee consumptive water users would pay

$5.98 per million gallons per year pumped to maintain pipes. Annual damages would be $3.37

million (di = 3.37).

Public ecosystem service loss

Surrounding Lake Okeechobee are 29,000 acres of Audubon Society wetlands and 31,000

acres of unnamed wetlands for a total of 60,000 acres of wetlands. Costanza, et al. (2003)

estimated the value of wetland services to be $1,083 per acre per year. Multiplying $1,083 by

60,000 acres yields a wetland damage estimate of $64.98 million per year (e = 64.98).

Private economic benefit

Between 1983 and 2002, anglers spent an average of 1,575,340 hours on Lake Okeechobee

each year (FFWCC, 2003). The Florida Fish and Wildlife Conservation Commission reported

average spending of $20.65 per hour in 2002 (FFWCC, 2003). Using total expenditures to

estimate the recreational value of freshwater fishing, we multiplied hours fished by value per

hour to obtain a total recreational value of $32.5 million per year. Assuming an increase in water

clarity attributable to zebra mussels would yield a 1% increase in fishing hours. The benefit from

zebra mussels is $0.325 million per year in state 4 (b = 0.325).

Management cost

A plan to monitor and prevent zebra mussels from entering Lake Okeechobee was

proposed in 2003 (U.S. Army Corps of Engineers, 2005). The plan included inspecting

underwater structures, sampling waterway sediments, and distributing education alert materials

to boaters, lake homeowners, and businesses. The cost of implementing the proposed plan is

$152,800 per year (cp = .1528).

In 2006, an infestation of zebra mussels prompted the Virginia Department of Game and

Inland Fisheries to pour 174,000 gallons of potassium chloride into Millbrook Quarry. At 100

parts per million the concentration was double the amount needed to kill zebra mussels but low

enough to avoid harming humans or fish. The single treatment is expected to protect the quarry

from zebra mussel infestation for 33 years. The cost for chemicals and labor was $365,000

(VDGIF, 2007). A similar treatment for Lake Okeechobee would require 628.6 million gallons

of potassium chloride at a cost of $1.320 billion. This cost annualized over 33 years is $55.03

million (c, = 55.03).

A summary of the parameter values used in the Zebra Mussel Model appears in Table 3.

Table 3. Zebra Mussel Model Parameter Values
Symbol Definition Value

all Probability of zebra mussel not being introduced to Lake Okeechobee 0.965

Probability of zebra mussel being accidentally introduced to Lake 0.035

a32 Probability of zebra mussel moving from state 2 to state 3 1

a43 Probability of zebra mussel moving from state 3 to state 4 1

a44 Probability of zebra mussel remaining state 4 1

all other a,i 0

b Economic benefits from zebra mussel $0.325 mil

Cp Cost of arrival prevention and monitoring (per year) $0.1528 mil

cr Cost of eradication (annualized) $55.03 mil

d, Private economic damages without mitigation expenditures (per year) $3.37 mil

d2 Private economic damages with mitigation expenditures (per year) $2.76 mil

d3 Private mitigation expenditures (annualized) $0.387 mil

e Value of wetland services lost with zebra mussels in state 4 (per year) $64.98 mil

fp Effectiveness of prevention measures 0.75

fr Effectiveness of eradication measures 1.00

r Discount rate 0.02

t Year 0,...,19

T Planning horizon 20 years

Four management scenarios

With Management I (do nothing) public management costs are zero. Private water users

become aware of zebra mussels when they incur damages d, in the first year of state 4. In the

second year they will apply anti-fouling paint thereby incurring damages d2 and d3 in subsequent

years. Public ecosystem loss is e for every year the system is in state 4. Public recreation benefit

is b for every year the system is in state 4.

With Management II (prevention), public management cost is cp when the system is in

state 1 and 2 and zero in states 3 and 4. Private damage is d3 during the first year that the system

is in state 3 and d2 and d3 while in state 4. Public ecosystem loss is e for every year the system is

in state 4. Public recreation benefit is b every year the system is in state 4.

With Management III (late eradication), public management cost is c, after the system

reaches state 4. Private water users become aware of zebra mussels when they incur damages d,

during the first year in state 4. In subsequent years private damages drop to zero because the

zebra mussels are eradicated. Public ecosystem loss is e for one year while the system is in state

4. Public recreation benefit is b for one year while the system is in state 4.

With Management IV (prevention and early eradication), public management cost is cp

while the system is in state 1 and 2, c, when the system is in state 3, and zero otherwise. Private

damage is zero. Public ecosystem loss and public recreation benefit are zero as the system never

reaches state 4.

The empirical zebra mussel model was run on GAMS software (GAMS, 1998). A

presentation and discussion of results follow.


The least cost strategy is Management I in which nothing is done to prevent zebra mussels

from entering Lake Okeechobee and nothing is done to arrest propagation after they arrive. Over

20 years management cost is $0. The present value of expected ecosystem damages in terms of

lost wetland functions is -$219.5 million. Private water users sustain -$25.7 million in expected

damages from increased maintenance expenditures and recreational anglers will gain +$1.1

million in expected fishing benefits. The net present value of"do nothing" is -$244.1 million.

The next least costly strategy is Management II in which prevention measures are

implemented. Since prevention is only 75% effective, if zebra mussels arrive, we assume

prevention measures would be halted and no further action would be taken to manage the

growing mussel population. Over 20 years, the present value of expected public expenditure on

prevention is -$2.5 million. The present value of expected ecosystem damages in terms of lost

wetland functions is -$62.4 million. Private water users will endure -$7.2 million in expected

damages due to increased maintenance and mitigation expenditures. Recreational anglers will

enjoy +$0.3 million in expected fishing benefits. The net present value of managing the threat of

zebra mussel with prevention is -$71.8 million, a gain of +$172.2 million over doing nothing.

The most costly strategy is Management III in which zebra mussels are eradicated from

Lake Okeechobee after they begin causing damage. Over 20 years, the present value of expected

public expenditure on eradication is -$185.9 million. The present value of expected ecosystem

damage in terms lost wetland functions is -$23.8 million. Private water users will absorb

expected damages of -$1.2 million and recreational fishers will gain +$0.12 million in expected

fishing benefits. The net present value of late eradication is -$210.8 million, a gain of +$33.3

million compared to doing nothing.

The strategy with the smallest public ecosystem loss, least private economic damage, and

the highest expected net present value is Management IV in which both prevention and

eradication measures are used to mitigate infestation and resulting damages. Over 20 years, the

present value of expected public expenditure on prevention and early eradication is -$55.4

million. Expected loss in ecosystem functions, damage to private consumptive use, and gain to

recreational anglers is $0. The net present value from prevention and early eradication is -$55.4,

a gain of +$188.7 million compared to doing nothing.

Among the four alternatives, the optimal strategy based on the net present value of

expected costs, damages, losses, and benefits over the 20-year planning horizon as defined in

equation 17 is Management IV Prevention and early eradication. A summary of the simulation

model results appears Table 4.

Table 4. Zebra mussel model simulation results

Management Alternative


Prevention and
Do nothing Prevention early

$ million

Public management cost

Public ecosystem loss

Private economic damage

Private recreational benefit



























T = 20 years, r = .02


Results show large gains to investment in prevention. With an expected outlay of $2.5

million for prevention measures over 20 years, more than $170 million in expected losses and

damages can be avoided. If a prevention program is not in place before zebra mussels are

introduced and begin causing damages, eradication may be warranted. Over 20 years, the

expected expenditure for eradication is -$185.9 million which would serve to reduce impending

damages by -$220 million. If a prevention program is in place and zebra mussels are detected

before the can cause damage, early eradication would serve to supplant -$70 million in expected

damages for an incremental cost of-$52.9 million over prevention alone.

Breakpoint parameter values

To test model robustness, we estimated breakpoint values for key parameters in the model.

Here we define breakpointt value" to be the value at which the relative preference of the four

management strategies changes based on expected NPV.

Simulation results show that if the annual probability of zebra mussel arrival was only

0.0004 (rather than 0.035), prevention would not be warranted. The optimal strategy would be to

wait for zebra mussels to arrive and eradicate them when they are detected.

If the probability that introduced zebra mussels will propagate and grow to critical mass is

0.052 (rather than 1), prevention would not be warranted. Instead, managers should eradicate

zebra mussels when they are detected.

Recreational water users may advocate reduced zebra mussel management. Our

simulations show that if the benefit from zebra mussels was instead $71.6 million per year

(compared to our assumed value of $0.325 million), the advantages of allowing zebra mussels to

enter Lake Okeechobee would out weight the projected damages. In this case, neither prevention

nor eradication would be warranted.

We found that if the annual cost of prevention ballooned to $8.7 million per year (versus

our assumed value of $0.1528 million), prevention would be unwarranted as there would be no

advantage over late eradication. There would however be a slight advantage to being able to

eradicate early versus late. Likewise, if the effectiveness of prevention at reducing the arrival rate

fell to 17% (versus 75%), there would be no gain in prevention over eradication. Finally, if

prevention cost was $9.7 million per year, early eradication would be unwarranted and late

eradication would be preferred.

If on the other hand the annual cost of eradication was $1,729 million per treatment (versus

$1320 million), neither late nor early eradication would be warranted. With high eradication

costs, prevention measures take on more importance as a means of mitigating potential damages.

As a reference, $1,729 million is equivalent to an annualized cost of $72 million per year for 33

years or the same treatment at $1,320 million lasting for only 15 years.

Estimated breakpoint values and the relative rankings of management alternatives appear

in Table 5.

Table 5. Breakpoint parameter values for zebra mussel model

Management Alternative
SDefi n Parameter Breakpoint I II IV
Symbol Definition Value Value
All Base model parameters Table 3 Table 3 4 2 3 1

a11 Annual probability of zebra mussel not arriving in Lake Okeechobee 0.965 0.99960 3 3 1 2

a21 Annual probability of zebra mussel arrival in Lake Okeechobee 0.035 0.00040

a32 Annual probability of zebra mussel moving from state 2 to state 3 1 .052 3 3 1 2

a43 Annual probability of zebra mussel remaining in state 3 to state 4 1 .052

a44 Annual probability of zebra mussel remaining in state 4 1 .052

b Benefit (to fishing from zebra mussel) $0.325 mil $71.6 mil 1 1 3 2

C1 Annual cost of prevention and monitoring $0.1528 mil $ 8.7 mil 3 2 2 1

C2 Eradication cost $55.03 mil $72.08 mil 2 1 3 1

Eradication cost (annualized) $1,320 mil $1,729 mil

7f Eradication duration (years) 33 15 2 1 3 1

e Value of wetland services (per year) $64.98 mil $48.09 mil 2 1 3 1

Value of wetland services (per acre) $1,083 $801.4 2 1 3 1

f Effectiveness of prevention measures 75% 1% 3 3 2 1

Rank = 1 implies the highest expected NPV


The zebra mussel is expected to reach Florida in the near future and thus poses a threat to

wetland ecosystem services and consumptive water uses. Several years ago the U.S. Army Corps

of Engineers responded to the threat by outlining an education, monitoring, and prevention

program for Lake Okeechobee. The program however was never funded. While bringing live

zebra mussels in the state of Florida is illegal and punishable by fine, there is no other state or

federal program to prevent zebra mussels from entering Lake Okeechobee. In lieu of prevention,

eradication post arrival is an option, albeit a costly one.

This study examined the potential impact of zebra mussels on ecosystem services,

consumptive water uses, and recreation in Lake Okeechobee. A probabilistic model was

developed to simulate the arrival and spread of zebra mussels and assess the cost effectiveness of

alternate management strategies. Results indicate that both prevention and eradication of zebra

mussels are economically justified for Lake Okeechobee.

These findings are based on the data we used to parameterize the model. While we used

the best data available to the study, some questions undoubtedly remain. To tackle these

questions head on and advance the dialog on this topic, we conducted a series of sensitivity tests

around key model parameters. Specifically we tested the probability that zebra mussels would

arrive in Lake Okeechobee and the likelihood that they would survive and reproduce in this new

environment. We also tested our assumptions on the effectiveness a prevention program that

would cost only $152,800 per year and brought into question the cost of a prevention program

that boasted 75% effectiveness. Because documented eradications of invasive mollusks are few,

we reexamined our assumptions regarding how much this action might cost presuming

eradication was technically feasible and environmentally desirable.

The battery of sensitivity tests were presented in the form of breakpoint values, i.e.

borderline values of the tested parameters that would cause a change in the relative ranking of

the preferred alternatives. Under the baseline model parameters, Management IV was most

preferred, that is offered the highest expected net present value. Next preferred were

Management II, III, and I. Our sensitivity tests showed that the cost effectiveness of prevention is

fairly robust over a wide range of model assumptions. For example, probability of arrival, habit

suitability, and prevention effectiveness would have to be many times smaller or the cost of

prevention would have to be many times larger to rule out prevention as a worthwhile public

investment. In contrast a mere 30% increase in the cost of eradication would cause this

management activity to be ruled out based on cost effectiveness. Likewise, it would only take a

26% reduction in projected wetland losses due to zebra mussels to conclude that eradication may

not be worthwhile.

To evaluate the eradication of zebra mussels from Lake Okeechobee we used case studies

from other locations to infer treatment procedures, chemical dosages, and overall cost. Better

information will be required before managers will embark on a venture of this magnitude.

Fortunately the decision to eradicate can be postponed until zebra mussels have arrived at which

time hopefully more will be known. Because of the likely arrival of zebra mussels, their potential

to induce economic and environmental damage and the uncertainty regarding the technical

feasibility and cost effectiveness of eradication, this study provides empirical evidence for

prevention as a sensible management option that is economically justified. While additional

scientific study could lend better data to improve the precision of our model estimates, the

imminent threat of zebra mussels will remain until a prevention program is in place.


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Table 6. Zebra mussel model simulation results (using HSI = .83)
Management Alternative


Prevention and
Do nothing Prevention early

$ million

Public management cost -$0 -$2.5 -$150.9 -$45.3

Public ecosystem loss -$178.2 -$50.6 -$19.5 -$0

Private economic damage -$20.9 -$5.9 -$1.0 -$0

Private recreational benefit +$0.9 +$0.3 +$0.1 +$0

NPV -$198.1 -$58.7 -$171.3 -$45.3

ANPV $0 +$139.4 +$26.8 +$152.8

T = 20 years, r = .02

Table 7. Zebra mussel model simulation results (using HSI = .91)
Management Alternative


Prevention and
Do nothing Prevention early

$ million

Public management cost -$0 -$2.5 -$167.3 -$50.1

Public ecosystem loss -$197.6 -$56.1 -$21.5 -$0

Private economic damage -$23.2 -$6.5 -$1.1 -$0

Private recreational benefit +$1 +$0.3 +$0.1 +$0

NPV -$219.8 -$64.9 -$189.9 -$50.1

ANPV $0 +$154.9 +$29.9 +$169.7

T = 20 years, r = .02

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