Ecological Economics 111 (2015) 100–110

Contents lists available at ScienceDirect

Ecological Economics
journal homepage: www.elsevier.com/locate/ecolecon

AnalysisTaking the sting out of Little Fire Ant in Hawaii
Donna J. Lee a,⁎, Michael Motoki b, Casper Vanderwoude c, Stuart T. Nakamoto d, PingSun Leung eaDept. of Natural Resources & Environmental Management, College of Tropical Agriculture and Human Resources, University of Hawaii at Manoa, DJL Economic Consulting, 2442 Kuhio Ave,
Honolulu, HI 96815, USAb
Dept. of Natural Resources & Environmental Management, College of Tropical Agriculture and Human Resources, Public Administration Program, College of Social Sciences, University of Hawaii
at Manoa, 98-459 Pono Street, Aiea, HI 96701, USAc
Hawaii Ant Lab, Paciﬁc Cooperative Studies Unit, RCUH, University of Hawaii, 16 East Lanikaula Street, Hilo, HI 96720, USAd
Dept. of Human Nutrition, Food & Animal Sciences, College of Tropical Agriculture and Human Resources, University of Hawaii at Manoa, 1955 E-W Road, Honolulu, HI 96822, USAeDept. of Natural Resources & Environmental Management, College of Tropical Agriculture and Human Resources, University of Hawaii at Manoa, 3050 Maile Way, Gilmore 111, Honolulu,
HI 96822, USAa r t i c l e

i n f oArticle history:
Received 8 June 2014
Received in revised form 15 January 2015
Accepted 22 January 2015
Available online xxxx
Keywords:
Bioeconomic modeling
Invasive species
Socio-economic impacts
Management
Little Fire Ant
Wasmannia auropunctata

a b s t r a c t
In the 1990's, Little Fire Ants (LFAs) found its way to the island of Hawaii, most likely traveling with a shipment ofpotted plants from Florida. These plants were subsequently sold to consumers along the east coast of the Island,along with Little Fire Ant colonies living in the potting medium. LFA is now thriving and continues to spread. Fifteen years after the initial detection in 1999, LFA has spread to over 4000 locations on the island of Hawaii and has
been found in isolated locations on Kauai, Maui, and Oahu Islands. Current efforts are expected to contain the infestations on the other islands but signiﬁcant additional investment is needed to halt the rapid spread of LFA on
the island of Hawaii.
Increased management expenditures can suppress infestations; reduce spread between sectors; and decreaselong-term management costs, damages, and stings.
• An immediate expenditure of $8 million in the next 2–3 years plus follow-up prevention, monitoring, and mitigation treatments will yield $1.210 billion in reduced control costs, $129 million in lowered economic damages, 315 million fewer human sting incidents, and 102 million less pet sting incidents over 10 years.
• Over 35 years, the beneﬁts include $5.496 billion in reduced control costs, $538 million less economic damages,
2.161 billion fewer human sting incidents, and 762 million fewer pet sting incidents.

© 2015 Published by Elsevier B.V.

1. Introduction
1.1. Problem Statement
Wasmannia auropunctata (roger), known as the Little Fire Ant (LFA),
threatens native biodiversity, alters tropical ecosystems, impairs humanhealth, impedes tourism, diminishes agricultural productivity, mars
horticulture sales, and accordingly ranks among the world's worst
invasive species (Lowe et al., 2000). Little Fire Ant will sting endangered
reptiles and birds, interfering with reproduction, nesting, and survival of⁎ Corresponding author.
E-mail addresses: DJL.DonnaJLee@gmail.com (D.J. Lee), motoki.ms@gmail.com(M. Motoki), CasperV@Hawaii.edu (C. Vanderwoude), SNakamo@hawaii.edu(S.T. Nakamoto), PSLeung@hawaii.edu (P. Leung).

http://dx.doi.org/10.1016/j.ecolecon.2015.01.010
0921-8009/© 2015 Published by Elsevier B.V.

young. They also sting cats, dogs and other domestic animals in the eyes,
blinding them over time (Theron, 2005). Humans are also stung by thisspecies, both indoors and outdoors. The sting typically causes an intenseburning sensation and painful itchy welts. Human habitats provide ideal
niches for Little Fire Ant growth and survival (Krushelnycky et al.,2005). Human activities disperse Little Fire Ant quickly and widely.
1.2. Research Statement1
The purpose of this research is to assess the long term impacts of Little Fire Ant in Hawaii and to ascertain the economic and social beneﬁt
from greater public investment in prevention and control.
We developed a multi-sector, dynamic, stochastic, bioeconomic
model to simulate LFA spread, human response, economic damages,
1

Abbreviations used in this article: LFA, HDOA.

D.J. Lee et al. / Ecological Economics 111 (2015) 100–110

and social impacts. We parameterized the model with government data,primary survey data, and information from experts and practitioners.
We speciﬁed several levels of management and simulated outcomeswith Microsoft Excel using Frontline Risk Solver Platform©.
1.3. Background
Ants were ﬁrst introduced when the Europeans settled the islands,
in the 18th century. Hawaii is now home to 47 introduced ant species(Krushelnycky et al, 2005); with the recent introduction Little Fire Ant
W. auropunctata regarded as potentially the most destructive. USDAARS (2010) estimate that total damages, losses and control costs attributed to invasive ﬁre ants in the United States is $5.6 billion per year.
Little Fire Ant arrived on the island of Hawaii most probably in the
1990's and by the time the infestation was detected in 1999 (Conantand Hirayama, 2000), Little Fire Ant had spread to 13 separate locations.
Aggressive control actions were undertaken immediately, however
Little Fire Ant continued to spread (Conant, 2002) and by 2004, infested
31 locations (Fig. 1). In the years following its initial detection, Little Fire
Ants have spread to three other islands in the Hawaii archipelago: Maui,
Kauai (Vanderwoude et al., 2010) and Oahu in late 2013.
The source of Little Fire Ants found in Hawaii is most likely Florida
USA. Little Fire Ants have an unusual form of reproduction. In introduced populations, almost all female reproductive offspring are genetically identical to the parent female and males are genetically identical tothe male parent. This clonal form of reproduction allows the source of
new invasive populations to be traced to the source population with ahigh degree of certainty. Foucaud et al. (2010) determined that the clonal lines of Little Fire Ants in Hawaii are identical to those of introduced
populations in Florida USA.
Due to the severity and extent of impacts, LFA is considered among
the world's worst invasive species (Lowe et al., 2000). In homes, schools,
lodging, and parks, Little Fire Ant will sting adults, infants, children andpets. The reaction to stings varies from person to person. Some people
experience a severe reaction with a great deal of pain and large raised
welts that itch for a week or more. Babies can receive numerous stings
within a few minutes of exposure. Pets are stung in the eyes and overFig. 1. Regions on Hawaii Island with one or more infested locations (red). (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web
version of this article.)101

several years lose their sight (Theron, 2005). Little Fire Ant infestations
put agriculture crops and workers at risk (Fabres and Brown, 1978).
When Little Fire Ant is present, aphid populations explode due tomutualism (Fasi et al., 2013) and farm workers are stung repeatedly.
Plant nurseries can and have gone out of business due to lost productivity, high treatments costs, and a reluctance by consumers to buy
infested stock. Wild honeybee hives in Hawaii have been swarmed
and destroyed by LFA.
Once established, Little Fire Ant can occupy their habitat at an extraordinarily high density. Souza et al. (2008) estimate that total population size can exceed 200 million ants per hectare with worker:queen
ratios of approximately 400 (Ulloa-Chacon and Cherix, 1990). Thisequates to a density of 20,000 ants per square meter, of which 40 will
be queens.
Best-practice mitigation activities for affected residents and businesses comprise a regular (six weekly) application of granular baits toexterior areas combined with the use of residual pesticides both insideand on the exterior of structures. The Hawaii Ant Lab (University of
Hawaii), with a staff of ﬁve people, provides research, outreach, education, training, advice and limited mitigation activities for all invasive ant
issues in the state of Hawaii including maintaining a website2 with information on impacts and remedies. The Big Island Invasive Species
Committee provides education and outreach on Little Fire Ant andother invasive species on the island of Hawaii.
In modeling invasive species management, Mumford and Norton(1984) applied Bayesian decision theory to determine the timing andlevel of management as a function of the invasive species population
density. Eiswerth and Johnson (2002) and Eiswerth and van Kooten(2002) incorporated dynamics to model population growth and uncertainty to allow for weather variability. To obtain closed-form solutions
to the optimal invasive species management problem, Burnett et al.
(2007), Carrasco et al. (2010), Mehta et al. (2007), Taylor andHastings (2004), and Olson and Roy (2003) assumed a continuous
rate of spread and employed optimal control modeling. Leung et al.
(2002) modeled discrete invasive species spread employing stochastic dynamic programming.
Prevention management including monitoring invasion pathways
associated with trade, transport and travel and inspecting potential
vectors was modeled by Perrings (2005). Olson (2006) modeled
invasive species introduction as a random variable and included prevention as a means to reduce the probability of introduction. Leunget al. (2002) speciﬁed prevention success as exponentially distributedand diminishing with effort. Mehta et al. (2007) indicated that prevention may do little to stop spread when the probability of introduction issmall or when the number of invasion pathways is large, and modeled
detection as a means of locating new introductions before they have
had a chance to spread, where the probability of detection increases
with the level of effort.
New introductions and established infestations require mitigation
treatment in the form of chemical, mechanical, and manual means to reduce or eliminate the infestation. Treatment effectiveness as a stochastic
process that decreases with effort was modeled by Feder (1979). The
effectiveness of successive treatments was modeled with a cumulative
probability distribution by Lichtenberg and Zilberman (1986). Olsonand Roy (2003) used dynamic programming to determine the conditions under which eradication, mitigation, and no mitigation are
optimal.
The marginal cost of invasive species management was modeled as alinear function that increased with the size of the infestation by Hastings
et al. (2006) and Burnett et al. (2007); as a convex function by Olson(2006); and as a budget constrained function by Taylor and Hastings(2004), and Hastings et al. (2006). The marginal economic damage
caused by the infestation was modeled as a linear function that2

www.littleﬁreants.com.

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D.J. Lee et al. / Ecological Economics 111 (2015) 100–110

increased with the size of the infestation by Gutrich et al. (2007); as aquadratic function by Burnett et al. (2007); and as a non-linear function
by Olson (2006) and Haight and Polasky (2010).
Leung et al. (2002), Burnett et al. (2007), and Eiswerth and vanKooten (2002) modeled invasive species population growth up to a carrying capacity over discrete time using a logistic function. Lee et al.
(2007) modeled invasive species growth and spread overtime using atransition matrix to forecast the probability of uninfested locations becoming invaded, and then tracking that status of the infestation from incubating, to propagating, to spreading to other locations. Carrasco et al.
(2010), Leung et al. (2002), and Burnett et al. (2007) simulated shortdistance dispersal via colony budding using a reaction–diffusion
model. Suarez et al. (2001), Souza et al. (2008), and Wilson et al.
(2009) modeled unlimited carrying capacity and long distance human
mediated dispersal. Nathan et al. (2003) used gravity models to quantify
human-mediated long distance dispersal. Hastings et al. (2005), andBossenbroek et al. (2001) used commerce and trafﬁc ﬂows to model
human-mediated dispersal pathways. Carrasco et al. (2010) assumed
outward dispersal via a random walk process and used diffusion
models. Eiswerth and van Kooten (2002), Kot and Schaffer (1986),
Hastings et al. (2005), and Law et al. (2003) employed a probabilistictransition function3 to model dispersal. Scanlan and Vanderwoude(2009) modeled dispersal using a stochastic cellular automata.
2. Materials and Methods
2.1. Model Framework
We simulate future spread and impacts from LFA on the island of
Hawaii using a bioeconomic model comprised of three integrated submodels: impact, management, and spread. Control variables determine
the level of effort allocated toward LFA detection, spread prevention,and mitigation treatment.
2.1.1. Impacts
The impact sub-model quantiﬁes economic impacts (economic
damage and management expenditure) and social impacts (the numberof human and pet LFA sting incidents) per sector over time. Economic
damages are sector dependent and vary with the size and extent of
the infestation. Management expenditures are based on best management practices and current technology and vary with management
goals, management effort, and the cost of labor and materials. Sting incidents are based on the number of infested locations in each sector,
human population, pet population, demographics, and employment ineach sector. A sting “incident” may involve multiple LFA stings.
2.1.2. Management
The management sub-model quantiﬁes the effect of management
decisions on LFA survival, growth and dispersal. Management activities
include detection, prevention, and mitigation treatment. Detection allows new infestations to be treated before they become established.
Prevention reduces the likelihood that LFA will be transported to another location by humans. Mitigation treatments reduce the intensity andextent of infestations.
2.1.3. Spread
The spread sub-model simulates LFA survival, growth and dispersal
as follows. When LFAs are initially introduced to a new location theirchance of surviving is low. If they survive, they go unnoticed for several
years during which they have time to establish and increase in number.
The ﬁrst year after introduction, LFAs are comparatively easy to eradicate. Once they establish, they are difﬁcult to eradicate, begin causing
3
A transition matrix is a kernel without a functional form, matrix elements denote theprobability of transitioning between states or spatial locations.

damage, and start producing new colonies that can be transported toother locations.
2.1.4. Original Contribution
In previous models of invasive ants, spatial spread was forecast using
radial and cellular speciﬁcations. Our approach is novel in that wemodel LFA spread within and across economic sectors over time. On
the island of Hawaii, LFAs are transported unintentionally by humans
with the movement of infested soil, produce, and other goods; mechanisms which do not follow a radial or cellular pattern. Further, LFA
nests are tiny compared with the area they can impact; several tiny
walnut-sized nests can disrupt the activities of an entire household or
farm. Thus rather than units of length or area, we use discrete locations
as our unit measure of “space”, e.g. a home, a school, a farm, and a park.
One unit represents one location. This pseudo-spatial approach provides us with a compact way of specifying and simulating the joint relationships between economic activity, LFA movement, LFA impacts(economic and social), and management response. Our second contribution is an accounting of the number of LFA stings and a comparisonof the Pareto tradeoff between economic impacts and stings.
2.2. Model Scope and Detail
Our model includes ninety thousand locations on the island of
Hawaii within seven economic sectors i ∈ {nursery, agriculture, lodging,residential, parks, schools, and all others}. Of the ninety thousand locations, 4581 locations are infested initially. Our model simulates infestation 35 years t ∈ {0…35} into the future. The number of locations per
sector and initial LFA infestation is shown in Table 1.
2.2.1. Impacts
Impacts from LFA comprise economic damages, management costs,
and human and pet sting incidents.
2.2.1.1. Economic Damages. Economic damages are sector-speciﬁc andvary with the size and extent of the LFA infestation. For example, in
the residential sector we include the impact of LFA on property values
when homes are sold. In the lodging sector we include reduced revenues from decreased room occupancy and cheaper room rates. The economic damage per sector location is based on estimated mean economic
impacts from LFA and is assumed to increase with the number of
infested locations and overall level of infestation. The economic damage
in sector i at time t is:establish 2
damage N i;t
:
Nmax
i

Di;t ¼ ci

ð1Þ

Table 1
Little Fire Ant infested locations on the island of Hawaii in 2012.
Sector% Infested

Infested locations

Total locations

Nursery
Agriculture
Lodging
Residential
Parks
Schools
Other
Total

22.5%
4.0%
0.2%
7.0%
3.9%
1.2%
1.7%
5%

170
186
1
3648
6
1
568
4581

757
4650
468
52,216152
84
32,547a90,874

From Motoki et al. (2013).ba
Hawaii Island is 2.58 million acres. With our 6 major sectors we account for 2.3 million
acres. Our sector “other” consists of 0.28 million acres and 81,556 parcels (according to2010 tax records). To scale the model, we represented the “other” sector with 32,547
locations.
b
Using data from the Hawaii Ant Lab; information from the 2007 Census of Agriculture,the 2011 Visitor Plant Inventory, City-data.com, and the State of Hawaii Data Book, and2013 PCSU Technical Report #186.

D.J. Lee et al. / Ecological Economics 111 (2015) 100–110

Here cdamageis the average economic damage at locations whereiis the number of locations
LFA has become established, N establish
i,twhere LFA has become established in sector i at the end of time t;
is the number of locations in sector i that are susceptible to LFA.
Nmaxi
= Nmaxand annual
Thus, when sector i becomes fully infested, Nestablish
i,t
i
max 4
N
.
damage is cdamageii
For agricultural impacts we estimated yield loss to untreated crops.
Agricultural damages are $600 per farm. For nursery impacts we estimated revenue losses due to banned exports. Nursery damages are$9000 per farm. For residential impacts we estimated reduced property
values when the homes are sold. Residential damages are $1000 per
property. For lodging impacts we estimated revenue losses due to reduced visitation and lowered rates. Lodging damages are $183,000 per
property. For park impacts we attempted to capture ecosystem productivity losses due to destruction of wild bee hives and increased chickmortality of ground nesting birds. Using cost transfer methods, park
damages are $2300 per acre. For “other” sector impacts we surveyed
landowners and businesses to ﬁnd out the most they would spend on
LFA mitigation. “Other” sector impacts are $500 per location.5
2.2.1.2. Management Expenditures. Management cost parameters are
based on current technology, best management practices, and current
costs for materials and labor. Total management expenditure is a function of management goals, management decisions, and size of the managed area. Management activities include prevention, detection, andmitigation.
Prevention expenditure is proportional to the number of infested
locations. Prevention expenditure cprevent is a function of unit cost
, number of known infested locations Nknown
and prevention efppreventii,tprevent
as follows:fort di,tprevent¼ci;tprevent known preventpi
N i;t di;t:ð2ÞDetection (monitoring) expenditure is proportional to the numberof uninfested locations. Detection expenditure is a function of the unit
, number of uninfested locations
cost of detection per location pdetect
i,t
known
detect− Ni,t), and detection effort di,tas follows:
(Nmax
i


detectdetectmax
known
detect¼ pi;tNi −Ni;tci;tdi;t :

mitigate

mitigate¼ pi

known mitigate
di;t:Expenditures for mitigation treatments, prevention, and detection
are summed to obtain total management expenditure in sector i attime t as follows:
prevent

Mi;t ¼ ci;tdetectþ ci;tmitigateþ ci;t:ð5Þ

2.2.1.3. Total Cost. Economic damage Di,t and management expenditure
Mi,t are discounted and summed over time t to obtain an expression of
the present value future total cost associated with LFA infestation:

Total Cost ¼

35
7
X
X
δt
Di;t þ Mi;t
t¼0

4
5

2.2.1.4. Social Impacts. LFA stings cause extreme pain, high anxiety, anditchy welts. While other species of ﬁre ants nest solely outdoors andon the ground, LFA will enter houses, nest under kitchen counters andin bedding, and crawl beneath clothing to sting people in their homes.
Outdoors, LFA can nest in leaf litter, in bushes, and in trees dropping
onto people who happen to brush by. Each encounter with LFA may entail multiple stings. Domestic animals and pets are particularly susceptible to LFA stings. In infested residential areas, LFAs have repeatedly
stung cats and dogs in the eyes inevitably blinding the animals overtime.
We used Census data (DEBDT, 2012a) and forecasts (DEBDT, 2009)
to estimate human population at home and at work (DEBDT, 2012b)
by sector. We used tourism authority data to estimate daily visitor
counts (HTA, 2012). We used U.S. pet statistics to estimate the population of domestic pets (cats and dogs) on the island of Hawaii (AVMA,
2012). We combined human and pet population data with our spread
model infestation rates to compute sting incidents to adults and children at home and at play, adults at work, children at school, and visitors
at lodging and at play. Using infestation in the residential sector, we estimated the number of sting incidents to domestic pets in homes.
The number of LFA sting incidents per year Si,t is dependent on the
Nestablishi;t, and the daily
Nmax
i
sting
probability of being stung in an infested area λi,t , multiplied by thehuman population Popi,t, the level of infestation,
number days per year:
human
sting establish
Si;t¼ λi;t Ni;t!
establish
Ni;t Popi;t 365:
Nmax
i

ð7Þ

Over 35 years, total human sting incidents is:
Total human sting incidents ¼

35 X
7
X
human
Si;t
:

ð8Þ

ð3Þ

ð4Þ

Ni;t

where δt = 1/(1 + r)t is the discount factor, r is the annual discount rate,and i indexes the seven economic sectors: agriculture, nursery, residences, schools, lodging, parks, and all others.

t¼0 i¼1

Mitigation treatments are applied to known infestations. Mitigation, numexpenditure cmitigate is a function of unit cost of mitigation pmitigateiknown
mitigate, and mitigation effort di,tas follows:
ber of infested location Ni,t
ci;t

103

Working conditions and land-use characteristics are all used to determine the sting incident rate λstingi,t . For example, nursery workers
who are in constant contact with plants will typically be stung more frequently than hotel workers. Sting incident frequency increases with theextent of LFA infestation. We quantiﬁed LFA sting incidents to humans
based on estimated number of human sting incidents that would
occur at homes, at work, in parks, at lodging, and at schools. We used
population data on residents, work force, and visitors.
The number of pet sting incidents per year is dependent on the number of domestic dogs and cats Poppets, pet sting incident frequency per
day λpets and level of infestation in the residential (homes) sector:
pet
pets
pets establish
St ¼ λ Popt N i;t

Nestablish
i;t
Nmax
i

!
 365:

ð9Þ

LFA human and pet stings are a major social concern. For this study,
we enumerate the number of sting incidents without monetizing themto allow the frequency of stings to be considered separately from economic impacts!

i¼1

The form of this equation is similar to Mehta et al. (2007).
About $50/acre per year.

ð6Þ

2.2.2. Management Decisions
Based on level of infestation, management goals and constraints, we
use the model to determine investment in prevention, detection, andmitigation by sector and time period. Investment in detection increases
the likelihood of ﬁnding LFA at newly introduced locations before theinfestation becomes established. Investment in prevention reduces the

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D.J. Lee et al. / Ecological Economics 111 (2015) 100–110

50%

47%

All sectors

45%
40%
33%

LFA infestaon

35%
30%

27%

25%
19% 19%

20%
15%

19%

13%
10%

10%
5%
0.40%

0.35%

0.12%

0.05%

0%
Least Cost
Current management
Reduced management

5

10

20

35

Year

Fig. 2. Little Fire Ant Infestation by management type and year across all sectors.

probability that LFAs are transported between locations. Investment in
mitigation reduces the level of infestation at established locations.

Detection investment ddetectis in units of person-hours per sector per i,tyear and lim θdetect
¼
1.
i;t

(…)
2.2.2.1. Decision Variables. The decision (control) variable, d i,t , deter-

Mitigation reduces the number of infested locations within a sector.
Here mitigation effort is measured in terms of the number of insecticide
per sector per year.7 Each application eradicatesapplications dmitigate
i,tsuch that
LFA with probability λmitigate
idmines the level of effort in prevention, detection, and mitigation ineach sector i at each time period t. Prevention and detection activities, ddetect≥ 0. Mitigation
are non-negative and unbounded, i.e., dpreventi,ti,tmitigate≤ 4.
treatment is nonnegative and bounded where 0 ≤ di,tdetect→∞ mitigate
mitigate di;t
¼ 1− 1−λimitigateand limdmitigate →4 θi;t
¼ ^θ:
mitigate

2.2.2.2. Effectiveness. LFAs are elusive and as a result management activities are imperfect. The annual probability that any management activity(prevention, detection, or mitigation) will succeed is less than one. We
model management success with a geometric distribution. Where λ isthe probability of success (e.g. preventing a new infestation at one location). For d ≤ 1, the probability of success is θ = 0, for d ≥ 1, and theprobability of success is:θ ¼ 1−ð1−λÞ

d

ð10Þ

where 0 ≤ λ ≤ 1 and 0 ≤ θ ≤ 1.
Prevention encompasses efforts to thwart new infestations by reducing movement of LFA between locations. Prevention effectivenessprevent
depends on the probability of stopping spread λpreventand the inθi,ti
prevent:
vestment in prevention di,tpreventθi;t preventprevent di;t
¼ 1− 1−λi:ð11ÞPrevention investment dprevent ∈ [0, ∞) is in units of person-hours
¼ 1.
per sector per year and preventlim θ prevent
i;t
d

→∞

Monitoring for LFA increases the likelihood that newly introduced
LFA colonies are found before they can establish, grow, and spread. Detection effectiveness θdetect
depends on the probability of detecting ani
6:
LFA infestation λdetect and investment in detection ddetecti,tdetectθi;t6 detectdetect di;t
¼ 1− 1−λi:ð12ÞThis formulation of early detection is a modiﬁcation of the functional form put forth by
Carrasco et al. (2010).

θi;t

ð13Þ

Management effort effectiveness parameters are derived from recommended best management practices and expert opinion.
2.2.3. Infested Locations and Spread
The initial infestation N starti,0 is set equal to the number of LFA infested(established) locations in 2012 as shown in Table 1. The spread submodel simulates the survival, growth, and dispersal of LFA over timewithin and between economic sectors. With this pseudo-spatial representation, we simulate LFA spread as occurring with the movement ofgoods and people over time within and across sectors. With informationon acres per unit (location) and units per sector, we estimate infested
acreage over time as follows: at each newly infested location the statustransitions from “introduced” to either “uninfested” or “incubating8”
and then to “uninfested” or “incubating” or “established.” The model
tracks the number of locations N in sector i at time t for each state of(…)
infestation (…) as given by Ni,t a whole number value that cannot
exceed the number of locations per sector deﬁned here as:
ð…Þ
ð…Þ
~ max :N ≥0 and ∑ N ≤ N
i;t

ð…Þ

i;t

i

2.2.3.1. Incubation, Detection, Mitigation. During incubation, LFAs reproduce but do not spread. The number of locations with incubating populations equals the number of locations infested from other sectors
Nintroduced
plus the number of locations infested internally Ngrowthi,ti,t − 1 .
While incubating, LFA can be detected with effectiveness θdetect. The
7
Insecticide application frequency is limited to 4 times per year per the manufacturer's
instructions.
8
Nascent.

D.J. Lee et al. / Ecological Economics 111 (2015) 100–110

number of locations with newly introduced (w = 1) incubating infestations that escaped detection is deﬁned:
incubateðunkÞ
¼
Ni;t;w
introduced
growthdetectN i;tþ Ni;t−11−θi;t:incubate
introduced
growthdetectþ Ni;t−1 θi;t :Ni;t;w ¼ Ni;tð15ÞIncubating infestations can be destroyed with probability λ = 1, so the
incubate= 1 then the Ni,t,w=0
decision to eradicate is d = (0, 1). If deradicate
i,t
eradicate= 0 the number of known locations with incubating populaIf di,ttions is deﬁned: Incubating infestations become established after
3 years. The number of locations with established LFA populations is
deﬁned:incubateincubate
eradicate
1−di;tNi;tþ1;wþ1 ¼ Ni;t;w
establish

Ni;testablish¼ Ni;t−1

þ Ni;t−1;3 þ Ni;t−1;3

:

ð17Þ

All established infestations are assumed to be “known” infestations
due to the damages they cause and are thus candidates for mitigation
treatment. The effectiveness of treatment θmitigate is deﬁned in
Eq. (13). The number of locations with established LFA colonies isdeﬁned:establish
establish¼ Ni;t−1
Ni;t
mitigate
1−θi;t:final

establish

incubateþ Ni;tincubateðunkÞ

þ Ni;toutestablish invasion
λi

:

ð19Þ



prevent1−θi;t:ð20Þ

Viable ant colonies transported into one sector from other sectors
are termed Incoming propagules Nini,t. Incoming propagules are thesum of Outgoing propagules Noutj,t transported from all other sectors
j ≠ i, deﬁned as follows:0in
Ni;t ¼ @Least cost

Current
management

Reducedmanagement

Least cost

Ag

1%

5%

7%

0.2%

19%

30%

Lodging

5%

50%

54%

0.4%

56%

67%

Nursery

1%

31%

39%

0.2%

43%

56%

Other

1%

8%

9%

0.1%

15%

23%

Parks

0%

60%

60%

0.1%

56%

66%

Residential

0%

11%

15%

0.0%

21%

32%

Schools

24%

52%

64%

0.2%

45%

57%

Sector

1!
n
X
Ngrowthout Ai;tk j;i  N j;t
1− max :
Ni
j

ð21Þ

The matrix K captures the commerce on the island likely to transport
ant colonies between sectors. The matrix elements kj,i are nonnegativen

0 ≤ kj,i ≤ 1 with values that sum to one ∑k j;i ¼ 1. Uninfested and lessjinfested sectors are assumed more susceptible to incoming propagules
N growth
than heavily infested sectors hence inclusion of the factor 1− Ni;tmax .
iPercent infested.

Of the incoming propagules only a proportion λsurvive
survive to becomeinewly introduced infestations:introduced

Ni;t

¼λ

surviveinNi;t :

ð22Þ

2.2.3.3. Intrinsic Growth. For our model, we deﬁne intrinsic growth as viable ant colonies crawling from one location to another. For LFA, the rateof intrinsic growth λgrowth is slow.10 We simulate intrinsic growth as inand decreasing in the number of established locations λgrowthNestablishi,tcreasing as the sector approaches full infestation. The number oflocations newly infested from intrinsic growth is deﬁned:
growth
growth establish
Ni;t
¼λ
Ni;t

!
Nestablish
i;t
:
1−
N max
i

ð23Þ

To assess the potential economic damages from Little Fire Ant on theisland of Hawaii and potential beneﬁts from managing Little Fire Ant,
we evaluated a current management (status quo) scenario and two alternate scenarios: reduced management (a reduction in public management efforts to contain infestations and prevent spread) and least cost(a theoretical Pareto optimum that assumes perfect knowledge andfull cooperation; the sum of management costs and economic damages
is minimized).
Current public management is led by the Hawaii Ant Lab (Universityof Hawaii). With a staff of ﬁve people, the Lab provides research, outreach, education, training, advice and limited mitigation activities for
all invasive ant issues in the State of Hawaii including maintaining a
website11 with information on impacts and remedies. The Big Island Invasive Species Committee provides education and outreach on Little
Fire Ant and other invasive species on the island of Hawaii.
For the current management scenario, we assumed that residents
and businesses with LFA infestations treat periodically to mitigate
local impacts but not sufﬁciently to eradicate LFA from their property
or halt the spread to other properties. Treatment occurs when infestation reaches 20%, then control effort is proportionate to the level of infestation. In the Park and School sectors, LFA infestations remain
untreated.12
For the reduced management scenario, we assumed a cut in publicfunding for mitigation treatment, prevention, detection, outreach andeducation which would result in a faster rate of spread. Residents andbusinesses with LFA infestations treat periodically to mitigate local impacts but not sufﬁciently to eradicate LFA from their property or halt
the spread to other properties. Treatment occurs when infestation
10

Ten meters per year.
www.littleﬁreants.com.
At present, infested public schools and parks are being treated for LFA. However, when
this study began, schools were not treated due to lack of funding and parks were not treated because use of anticides was not permitted.
11
12

9

Current
Reducedmanagement management

3. Management Scenarios

2.2.3.2. Human Transport. Through human movement (to and fromwork, school, and outdoor recreation) and goods exchange, live viable
ant colonies are dispersed among and between sectors.
Viable ant colonies transported out of one sector to another sector istermed an Outgoing propagule. The number of Outgoing propagules
invasion 9
to the number of infested locations
Nouti,t is proportionate λiestablish
less the effectiveness of prevention efforts θ prevent
and isNi,ti,texpressed as follows:
Ni;t ¼ Ni;t

Year
35

ð18Þ

The number of infested locations in each sector i is:
Ni;tþ1 ¼ Ni;t

Year
5

ð16Þ

incubate ðunkÞ

incubate

Table 2
Little Fire Ant Infestation by sector in years 5 and 35.

ð14Þ

The number of newly introduced incubating infestations that havebeen detected (w = 1) is deﬁned:

105

Termed “base rate invasion probability” (Leung et al., 2002).

106

D.J. Lee et al. / Ecological Economics 111 (2015) 100–110

120
107

Human sting incidents (million)

All sectors
100
86
80

79
80

74

60

53
46
40

40

20
7.10

6.31

0.49

0.21

0
Least cost

5

10

Current management

20

35

Year

Reduced management
Fig. 3. Little Fire Ant human sting incidents by management type and year across all sectors.

reaches 20%, then control effort is proportional to the level of infestation. In the Park and School sectors, LFA infestations remain untreated.
For the least cost management scenario, we assumed that treatment
decisions in all sectors were made to beneﬁt the whole island without
regard to distributional effects.
We applied simulation modeling to determine the long-term impacts from current management and reduced management.13 We
applied optimization modeling to determine the cost minimizing decisions and long term impacts from least cost management.
The model was run on Microsoft Excel using the Frontline Risk Solver Platform.

expenses and $11 million in damages. Mitigation expenditures are
greatest in the agriculture and school sectors. Prevention expenditures
are greatest in the residential sector. Detection expenditures are
greatest in the lodging sector. Over 35 years, the total number of Little
Fire Ant sting incidents involving children, adults and visitors is
94 million.
4.3. Reduced Management

Under current management in the coming 5 years, Little Fire Ant will
spread on the island of Hawaii infesting 31%, 50%, 60%, and 52% of thenursery, lodging, park, and school sectors. In 10 years, infestation willreach 42% and 54% in the nursery and lodging sectors. In 35 years, thepresent value total cost from Little Fire Ant is $6.1 billion based on$5.536 billion management expenditures and $549 million in economic
damages. Costs are greatest in the agriculture, park, and school sectors.
Over 35 years, the total number of Little Fire Ant sting incidents involving children, adults and visitors is 2.3 billion.

Under reduced management, in the coming 5 years, Little Fire Ant
will spread more quickly on the island of Hawaii infesting 53%, 66%,
71%, and 54% of the nursery, lodging, park, and school sectors. In
10 years, infestation will reach 57%, 71%, 74% in the nursery, lodging,and park sectors. Mitigation expenditures are greatest in the agriculture,park, and school sectors. The number of sting incidents is highest in theresidential sector. In 35 years, the present value total cost including
management expenditures and economic damages from Little Fire Ant
is $12.9 billion. Over 35 years, the total number of Little Fire Ant sting incidents involving children, adults and visitors is 2.8 billion.
Simulation model results for infestation over time by sector andmanagement type are illustrated in Fig. 2 and Table 2.
Simulation model results for human sting incidents over time by sector and management type are illustrated in Fig. 3 and Table 3.
Simulation model results for total cost over time by sector and management type are illustrated in Fig. 4a–c.

4.2. Least Cost Management

4.4. Management Tradeoffs

To achieve least cost management, Little Fire Ant is suppressed withearly mitigation treatment; prevention and detection in all infested sectors. Under least cost management in the coming 5 years, Little Fire Ant
infestations decrease to 5% and 24% in the lodging and school sectors,
drop to 2.5% in the nursery and lodging sectors, and sink to 1% orlower in the remaining sectors. Over 35 years, the present value total
cost is $51 million based on an estimated $40 million in management

We conducted a multi-objective analysis to evaluate the tradeoff between management focused on reducing the monetary cost of an LFA
infestation (management expenditures and damages) versus management focused on reducing the number of human sting incidents. If
cost reduction is the primary objective, a least cost management strategy will yield a PV total cost of $51 million and 94 million human sting
incidents over 35 years. This outcome is a clear improvement overcurrent management,14 as both cost and human sting incidents are
reduced. This outcome is “efﬁcient” because in order to further reduce

4. Results
4.1. Current Management

13
We applied simulation modeling. For interested readers, a comparable problem solved
with constrained optimization would minimize LFA spread subject to a public budget of$200k to depict current management and minimize LFA spread subject to an annual budget of $100k to depict reduced management.

14
Under current management PV total cost is $6.1 billion and total human sting incidents is 2.3 billion over 35 years.

D.J. Lee et al. / Ecological Economics 111 (2015) 100–110

over 35 years. This outcome is a clear improvement over current management, as both cost and human sting incidents are reduced. This outcome is “efﬁcient” because in order to further reduce sting incidents
costs would have to rise. For example, reducing human sting incidents
to 22 million will cost $140 million over 35 years for a marginal costof $3 per human sting incident avoided. Reducing human sting incidents
to 6 million will cost $944 million over 35 years for a marginal cost of$306 per human sting incident avoided. Additional numerical resultsfrom the multi-objective analysis can be seen in Table 4.
If society places a high value on avoiding sting incidents, i.e. not getting stung, they may be willing to invest more in LFA management andtreatment. Information on marginal costs can help individuals determine their preferred level of LFA control. At higher costs, individuals
may prefer to be stung rather than pay for the additional management.
Efﬁcient alternatives for the island of Hawaii range from $2 to $306 per
avoided sting incident. Values are displayed in Table 4 and illustrated inFig. 5.

Table 3
Little Fire Ant human sting incidents by sector in years 5 and 35.
Year5
SectorLeast cost

Year
35

Current
Reducedmanagement management

Least cost

Current
Reducedmanagement management

Ag

0.01

0.03

0.05

0.00

0.26

0.41

Homes

0.00

8.46

11.11

0.00

25.24

38.79

Lodging

0.74

6.79

7.29

0.10

14.33

17.35

Nursery

0.01

0.23

0.30

0.00

0.59

0.76

Other

0.14

1.50

1.76

0.03

4.97

7.81

Parks

0.07

11.27

11.24

0.02

17.80

21.22

Schools

5.34

11.58

14.02

0.06

16.34

20.87

107

Million sting incidents.

costs, sting incidents would have to rise. If reducing human sting
incidents is the primary objective, a least sting management strategy
will cost $91 million and reduce human sting incidents to 73 millionaAll sectors

Management expenditure (2012 $ million)

$9

$8

$8
$7

$7

$7
$6
$5
$4
$3
$2

$2
$2
$1
$0

$0

$0

$0

$0
Least cost management
Current management
Reduced management

b

1

2

3

Year
All sectors

$300

$284

$275

$260
$247

Total cost (2012 $ million)

$250

$228
$193

$200
$161
$150

$134

$100

$50
$0.58

$0.90

$0.44

$0.24

$0
Least cost management
Current management
Reduced management

5

10

20

35

Year

Fig. 4. a. Early management expenditures by year and management type. b. Economic cost to society by year and management type. c. Little Fire Ant total economic cost over 35 years bymanagement type.

108

D.J. Lee et al. / Ecological Economics 111 (2015) 100–110c

Total cost ($millions)$12,880$6,085$51
Least Cost

Current management

Reduced Management

Fig. 4 (continued).

5. Discussion of Results
Our model results showed that an increase in funding over current
management will be needed to prevent rapid and widespread infestation of Little Fire Ant on the island of Hawaii.
The beneﬁts from increased management effort include:• Improved quality of life for residents, children, and pets.
• Savings to homeowners from less frequent treatment of LFA in andaround the home.
• Protection to agricultural and nursery farms from large increases in
expenses and potential economic losses due to yield decline, treatment costs, lost sales, and reduced export volume.
• Protection to visitor industry businesses from large increases in expenses and potential economic losses due to visitor sting incidents
on lodging property and at popular outdoor recreation areas.
• Reduced risk of spread from the island of Hawaii to other islands in theState.
Technical challenges in managing little ﬁre ant on the island of
Hawaii include:• Newly developed bait formulations and application methods areproving effective in controlling LFA populations. However their use
in commercial agriculture is banned except for a few food crops.
• LFAs are thriving in beach parks, but until recently no chemical options were permissible for use at infested locations near water.

Economic Challenges and Opportunities• Treating a widespread infestation of LFA will require a high level ofcooperation from all agents including property owners, farms, businesses, and multiple levels of government. In our model, we assumed
full cooperation, but in reality that is not be the case. We've heard several complaints from distressed homeowners and farmers about LFA
infestations on neighboring properties that are left untreated.
• At the private level, individual households and businesses will pay tocontrol LFA on their own property hence beneﬁting their neighbors,
however since they do not share in those additional beneﬁts, they
will then tend to underinvest in LFA control, perhaps not treating
the periphery of their property or otherwise leaving more ants than
optimal to reproduce and spread (Positive externality).
• The location of new infestations is difﬁcult to predict. To a large extent,
the State relies on an observant public to report new infestations —detection through use of peanut butter sticks, visual observations, orreceiving stings (Imperfect information).
• Infested businesses may treat for LFA but be unwilling to report theirinfestation to avoid repercussions such as loss in customers, ban onsales, lost certiﬁcation, and quarantine (Asymmetric information).
• Neighborhoods, communities, and businesses within the same industry can share information, treatment methods, and costs, and beneﬁt
as a group from managing LFA collectively. Coordinating a group effort
requires a lot of communication, time, and willing volunteers (Information costs, scale economies, positive externalities).

6. Conclusions
On the island of Hawaii, Little Fire Ant infests over 4000 locations.
Current management includes ant species identiﬁcation, response, public information and assistance, technology development, public awareness and education. Our ﬁndings show that current management isslowing Little Fire Ant spread but will be insufﬁcient in preventing Little
Fire Ant from rapidly spreading within the island of Hawaii. Reducing
efforts to control Little Fire Ant will lower costs in the short term compared with current management, but lead to more sting incidents,

Table 4
Total cost and total human sting incidents over 35 years.
PV total cost

Human sting incidents

Marginal cost per avoided sting incidenta

$ mil

mil

$

$51
$91
$140
$153
$159
$166
$174
$183
$194
$207
$225
$254
$300
$388
$944

94
73
22
18
17
15
14
13
12
12
11
10
9
8
6

–
$2
$3
$4
$5
$6
$7
$9
$12
$16
$24
$41
$56
$83
$306

a
Marginal cost is calculated as Increase in total cost ÷ Reduction in sting incidents fromthe row above. For example ($91 − 51) ÷ (94 − 73) = $2.

$ per sting incident avoided

D.J. Lee et al. / Ecological Economics 111 (2015) 100–110

$350
$300
$250
$200
$150
$100
$50
$0

109

Marginal cost

0

2

4

6

8

10

12

14

16

18

Total human sng incidents in millions
Fig. 5. Marginal cost per avoided human sting incident.

higher costs and larger damages in the longer term. Results indicate thatan increase in management effort is economically and socially warranted as the island economy would realize net beneﬁts of $5 billion in total
cost savings including a reduction in economic damages of $540 million
and avoidance of 2.1 billion human sting incidents over 35 years.
7. Summary
Management effort has a signiﬁcant impact on Little Fire Ant infestation over time. Under current management, Little Fire Ant infestation
will continue to rise in all sectors eventually becoming established inall sectors and in all developed locations on the island in 15 years. By increasing management effort through monitoring, spread prevention,and mitigation, Little Fire Ant spread can be slowed and populations
eventually suppressed. Under least cost management, Little Fire Ant infestations are suppressed over the course of 27 years.
Management effort has a signiﬁcant impact on the number of Little
Fire Ant sting incidents. Under current management, people on the island of Hawaii will suffer 2.3 billion sting incidents over 35 years.
Their pets will endure 0.9 billion sting incidents over 35 years. With efforts to suppress Little Fire Ant populations, under least cost management during the next 35 years people and pet will suffer fewer sting
incidents, down to 94 million for people and 9 million for pets.
Management effort has a signiﬁcant impact on costs and damages. In
the next 35 years the cost of Little Fire Ant under current management
will balloon to $6.1 billion. With efforts to suppress Little Fire Ant populations, under least cost management, net costs drop to $51 million, asubstantial savings to the local economy.
Acknowledgments
This research was supported in part by the Tropical and Subtropical
Agriculture Research (TSTAR) Program (Award Number 2010-3413521228), the National institute of Food and Agriculture (NIFA), U.S. Department of Agriculture (USDA). We graciously thank all the people
who generously responded to our request for help: our collaboratorsand cooperators; and the people who took the time to answer questions, respond to our questionnaires, and provide us with insight and information. Listed alphabetically by ﬁrst name we thank: Chi Ming Chan,
Christy Martin, Dave Lau, Diki Short, Eric Loève, Hervé Bossin, Jean-Yves
Meyer, Judy Schilling, J. Kenneth Grace, Kimberly Burnett, Lissa Fox
Strohecker, Lloyd Loope, Maryline Simon, Michelle Montgomery, Page
Else, Pat Conant, Robert La Mont, Rogerio Menescal, Rudolph Putoa,
Steve Shropshire, Teya Penniman, and Tina Yamaki. We are gratefulfor the comments and suggestions from two anonymous reviewers
which helped us improve the clarity of the article.
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