Dispersal of invasive forest insects via recreational firewood: a quantitative analysis.

Abstract

Recreational travel is a recognized vector for the spread of invasive species in North America. However, there has been little quantitative analysis of the risks posed by such travel and the associated transport of firewood. In this study, we analyzed the risk of forest insect spread with firewood and estimated related dispersal parameters for application in geographically explicit invasion models. Our primary data source was the U.S. National Recreation Reservation Service database, which records camper reservations at > 2,500 locations nationwide. For > 7 million individual reservations made between 2004 and 2009 (including visits from Canada), we calculated the distance between visitor home address and campground location. We constructed an empirical dispersal kernel (i.e., the probability distribution of the travel distances) from these "origin-destination" data, and then fitted the data with various theoretical distributions. We found the data to be strongly leptokurtic (fat-tailed) and fairly well fit by the unbounded Johnson and lognormal distributions. Most campers ( approximately 53%) traveled <100 km, but approximately 10% traveled > 500 km (and as far as 5,500 km). Additionally, we examined the impact of geographic region, specific destinations (major national parks), and specific origin locations (major cities) on the shape of the dispersal kernel, and found that mixture distributions (i.e., theoretical distribution functions composed of multiple univariate distributions) may fit better in some circumstances. Although only a limited amount of all transported firewood is likely to be infested by forest insects, this still represents a considerable increase in dispersal potential beyond the insects' natural spread capabilities.

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FOREST ENTOMOLOGY
Dispersal of Invasive Forest Insects via Recreational Firewood:
A Quantitative Analysis
FRANK H. KOCH,1,2DENYS YEMSHANOV,3ROGER D. MAGAREY,4AND WILLIAM D. SMITH1
J. Econ. Entomol. 105(2): 438Ð450 (2012); DOI: http://dx.doi.org/10.1603/EC11270
Recreational travel is a recognized vector for the spread of invasive species in North
America.However,therehasbeenlittlequantitativeanalysisoftherisksposedbysuchtravelandthe
associated transport of Þrewood. In this study, we analyzed the risk of forest insect spread with
Þrewoodandestimatedrelateddispersalparametersforapplicationingeographicallyexplicitinvasion
models. Our primary data source was the U.S. National Recreation Reservation Service database,
which records camper reservations at ?2,500 locations nationwide. For ?7 million individual reser-
vations made between 2004 and 2009 (including visits from Canada), we calculated the distance
betweenvisitorhomeaddressandcampgroundlocation.Weconstructedanempiricaldispersalkernel
(i.e.,theprobabilitydistributionofthetraveldistances)fromthese“origin-destination”data,andthen
Þtted the data with various theoretical distributions. We found the data to be strongly leptokurtic
(fat-tailed) and fairly well Þt by the unbounded Johnson and lognormal distributions. Most campers
(?53%) traveled ?100 km, but ?10% traveled ?500 km (and as far as 5,500 km). Additionally, we
examined the impact of geographic region, speciÞc destinations (major national parks), and speciÞc
originlocations(majorcities)ontheshapeofthedispersalkernel,andfoundthatmixturedistributions
(i.e., theoretical distribution functions composed of multiple univariate distributions) may Þt better
in some circumstances. Although only a limited amount of all transported Þrewood is likely to be
infestedbyforestinsects,thisstillrepresentsaconsiderableincreaseindispersalpotentialbeyondthe
insectsÕ natural spread capabilities.
ABSTRACT
KEY WORDS
distance dispersal
biological invasion, Þrewood, invasive forest pest, human-mediated dispersal, long-
The potential for accidental, long-distance transport
of invasive insects and pathogens in untreated Þre-
wood has become a topic of considerable concern in
North America (Haack et al. 2010, Tobin et al. 2010).
Theissuehasbeenthesubjectofnational-scalepublic
awareness campaigns in both the United States and
Canada (e.g., see Canadian Food Inspection Agency
[CFIA] 2011, The Nature Conservancy 2011), as well
as similar campaigns by individual states and prov-
inces. Recently, the USDA Animal and Plant Health
Inspection Service (APHIS) released a comprehen-
sive risk assessment of the movement of Þrewood in
the United States (USDA-APHIS 2011b), and also re-
quested comments on recommendations issued by a
National Firewood Task Force regarding regulatory
measures, voluntary activities, and outreach efforts at
the state and national levels (USDA-APHIS 2010).
Currently, a majority of U.S. states have imposed re-
strictions on Þrewood movement, in some cases en-
forced with Þnes and/or other penalties for violations
(The Nature Conservancy 2011). In Canada, any per-
son who moves Þrewood out of an area regulated for
aquarantinepestwithoutapprovalfromtheCanadian
Food Inspection Agency is subject to Þnes and/or
prosecution (CFIA 2011).
In the United States, discussion about the risks asso-
ciated with Þrewood movement essentially began in
August 1996, when the Asian longhorned beetle,
Anoplophora glabripennis (Motschulsky) (Coleoptera:
Cerambycidae), was discovered in the Brooklyn bor-
ough of New York. Shortly thereafter (September
1996), a second infestation was found in Amityville,
NY, ?50 km east of the Þrst detection (Haack et al.
1997). Although the Brooklyn infestation probably
originated through international trade (i.e., from in-
fested wood packing materials associated with im-
ported cargo), it is thought that A. glabripennis may
have been introduced to Amityville when infested
tree sections were transported from Brooklyn for sale
as Þrewood. In fact, fear of the likelihood of such a
scenario is what prompted surveyors to investigate
relatively distant areas such as Amityville after the
1USDA Forest Service, Southern Research Station, Eastern Forest
Environmental Threat Assessment Center, 3041 Cornwallis Road,
Research Triangle Park, NC 27709.
2Corresponding author, e-mail: fhkoch@fs.fed.us.
3Natural Resources Canada, Canadian Forest Service, Great Lakes
Forestry Centre, 1219 Queen Street East, Sault Ste. Marie, Ontario,
P6A 2E5, Canada.
4Center for Integrated Pest Management, North Carolina State
University/USDA Animal and Plant Health Inspection Service, Plant
Protection and Quarantine Division, Center for Plant Health Science
and Technology, 1730 Varsity Drive, Suite 300, Raleigh, NC 27606.

Page 2

initial discovery (Haack et al. 1997). Since the natural
dispersal potential of A. glabripennis is relatively low
(Smith et al. 2001, 2004), human activities including
Þrewood transport are also assumed to have been
responsiblefortheinsectÕsspreadtootherpartsofthe
New York metropolitan area, and likewise, for its
spread in Chicago (IL), Worcester (MA), Toronto
(ON),andBethel(OH),acommunity?50kmsouth-
east of Cincinnati (USDA-APHIS 2011a).
TheA.glabripennisexamplenotwithstanding,apri-
mary impetus for the current focus on Þrewood has
been the invasion of eastern North America by the
emeraldashborer,AgrilusplanipennisFairmaire(Co-
leoptera: Buprestidae). Native to Asia, A. planipennis
wasÞrstdetectedin2002nearDetroit(MI)andneigh-
boringWindsor(ON)(Haacketal.2002).Ithassince
been found in 14 other U.S. states as well as the prov-
ince of Quebec (National Agricultural Pest Informa-
tion System [NAPIS] 2011); movement of infested
Þrewood has been strongly implicated in the insectÕs
range expansion (Petrice and Haack 2006). Because
all North American ash (Fraxinus sp.) tree species are
susceptible, the economic impact of A. planipennis is
expectedtobesubstantial.Forthe10-yrperiod2009Ð
2019,theanticipatedtreatment,removal,andreplace-
ment costs for ash trees on developed land in U.S.
communities (i.e., costs not including forestland im-
pacts) have been estimated at greater than $10 billion
(Kovacs et al. 2010).
Firewood is relevant as a vector for other high-
proÞleforestpests,primarilywood-boringinsects(es-
pecially Coleoptera species). For instance, the move-
ment of Þrewood from Mexico is believed to have led
to the establishment of Agrilus prionurus Chevrolat, a
major pest of Western soapberry (Sapindus saponaria
varietydrummondii),inTexas(Haack2006).Notably,
long-distance transport of Þrewood for recreational
purposes appears to be a fairly common occurrence.
Haacketal.(2010)reportedonamulti-yearsurveyof
drivers who surrendered Þrewood at MichiganÕs
Mackinac Bridge. (Transport of Þrewood across this
bridge between the stateÕs Upper and Lower Penin-
sulas is prohibited under a A. planipennis quarantine.)
Accordingtothesurvey,16%ofvehiclessurrendering
Þrewood were from out of state, while 1% of vehicles
werefromCanada.Additionally,campgroundsurveys
in various parts of the United States indicate that
8Ð57% of campers bring their own Þrewood from
home, frequently traveling distances of 160Ð320 km
and crossing state lines (USDA-APHIS 2011b).
Whereas such Þndings are informative, they are
insufÞcient to quantify the nationwide potential for
long-distancedispersalofforestinsectsinrecreational
(i.e., camper-transported) Þrewood. In short, the
combinedresultsofthesesurveysdonotfullydescribe
the probability of Þrewood being transported over
certain distances (i.e., how far, and how often, Þre-
wood-carrying campers can be expected to travel),
particularly long distances. This latter limitation is
signiÞcant: Long-distance dispersal events substan-
tially increase the rate of spread of organisms, espe-
cially at larger (e.g., regional) spatial scales (Higgins
et al. 2003, Nathan et al. 2003). Notably, for many
invasive species, these instances of long-distance dis-
persal are almost exclusively associated with human
transport activities (Hastings et al. 2005).
Predictive models of the spatial spread of invasive
species can be informative for decision makers who
must implement regulatory and control measures de-
spite incomplete information and scarce resources
(Neubert and Parker 2004). However, reliable esti-
matesoftherateandextentoflong-distancedispersal
events are necessary to accurately model spread for
most invaders (Suarez et al. 2001, Hastings et al. 2005,
Pitt et al. 2009). Long-distance dispersal is especially
important from a pest management perspective be-
cause it may lead to the formation of satellite popu-
lations, which (although they may greatly increase an
invaderÕs overall rate of expansion) are more easily
controlled than large populations within the main in-
vasion front (Lockwood et al. 2007). Unfortunately,
because long-distance dispersal events are rare, em-
pirical data about them are difÞcult to obtain (Clark
etal.1998,Hovestadtetal.2001,BrownandHovmøller
2002, Higgins et al. 2003, Hastings et al. 2005), and in
turn,model-basedestimatesoftheirlikelihoodtendto
be highly uncertain (Nathan et al. 2003). The long-
distance dispersal potential of Þrewood has been de-
picted in some spatially explicit invasion models, par-
ticularlyforA.planipennis(BenDorandMetcalf2006,
BenDor et al. 2006, Muirhead et al. 2006, Prasad et al.
2010, Harwood et al. 2011), but only in a simpliÞed
(i.e.,theoretical)fashionorbasedonlimitedempirical
data. Typically, these and other invasion models in-
corporate the concept of stratiÞed diffusion (Hen-
geveld 1989, Shigesada et al. 1995, Nathan et al. 2003,
Lockwood et al. 2007), which acknowledges that spe-
cies may spread by more than one process (e.g., nat-
ural as well as human-mediated dispersal). Subse-
quently, each process may be modeled with an
individualprobabilitydistributionfunction(“kernel”)
thatdepictsthelikelihoodofdispersalviathatprocess
over a range of distances during a speciÞed time in-
terval. Instead, some models use “mixed kernels” that
integratefunctionsrepresentingbothshort-andlong-
distance dispersal processes (see Higgins et al. 2003,
Nathan et al. 2003). In either case, long-distance dis-
persal processes such as the movement of forest pests
inÞrewoodtypicallyrequireapplicationofleptokurtic
(also called fat- or long-tailed) functions that are
suited to representing the greater occurrence of rare
events (Kot et al. 1996, Nathan et al. 2003). For in-
stance, negative exponential or power law functions
have been regularly applied to depict long-distance
dispersal in theoretical models of biological invasions
(Cannas et al. 2006), including sophisticated spatial
simulations (e.g., Carrasco et al. 2010).
Given that a data-driven approach is preferable to
other methods (e.g., based on expert judgment) for
estimating dispersal probabilities (Quigley and Revie
2011), it would be beneÞcial if sufÞcient data were
available as an empirical foundation for deÞning ap-
propriate distance-dependent distribution functions
to represent Þrewood dispersal potential in invasion
April 2012KOCH ET AL.: DISPERSAL OF INVASIVE FOREST INSECTS IN FIREWOOD
439

Page 3

modeling efforts (i.e., as one particular long-distance
component of a stratiÞed diffusion framework). Al-
though data on Þrewood transport and utilization are
lacking in this regard, an alternative is to undertake a
moregeneralapproachbyexploringthetravelbehav-
iorofcampersratherthantheiractualuseofÞrewood.
For this study, we had the opportunity to analyze an
extensive (multi-year and national-scale) and geo-
graphically referenced database of campground visits
in the United States. Our primary objective was to
develop realistic, empirically based dispersal kernels
for describing key patterns of camper travel under
various scenarios (e.g., travel to speciÞc popular des-
tinations). In turn, by incorporating the limited avail-
ableinformationaboutÞrewoodusage,wealsohoped
to provide basic estimates of the potential contribu-
tion of recreational Þrewood movement to the spread
of invasive forest insects in the United States.
Materials and Methods
We performed all statistical analyses in the R soft-
ware environment (R Development Core Team
2011),insomecasesusingspeciÞcdeveloper-contrib-
uted analytical packages (individually cited below).
WeusedArcGIS9.3software(EnvironmentalSystems
Research [ESRI] 2009a) to perform all geospatial
analyses.
Campground Visitation Data. Our primary data
source for this study was the National Recreation
Reservation Service (NRRS). The NRRS handles res-
ervations for campgrounds and other recreational fa-
cilitiesoperatedbytheU.S.ArmyCorpsofEngineers,
the Bureau of Land Management, the Bureau of Rec-
lamation, the USDA Forest Service, and the National
Park Service. Members of the public (including indi-
viduals from outside the United States) can make
reservations at these facilities through the NRRS on-
line portal (http://www.recreation.gov), by tele-
phone, or at speciÞc Þeld ofÞces. Notably, the NRRS
does not manage reservations for all federal recre-
ational facilities, as a small percentage (e.g., facilities
in certain national parks) have independent reserva-
tion systems. However, NRRS-managed facilities are
well distributed across the United States.
We used NRRS reservation records spanning the
period from January 2004 to September 2009; these
data were previously procured from the NRRS by
USDA APHIS-Plant Protection and Quarantine
(PPQ). Each record included the following variables:
visitororiginstateandZIPcode,nameandstateofthe
destinationcampground,reservationdate(monthand
year), the number of reservations, and the number of
nights. The latter two variables represent summations
of the raw data by NRRS (at the request of USDA
APHIS-PPQ) in cases where records were identical
with respect to the other variables (i.e., records with
the same visitor origin, destination campground, and
reservation date).
Before analysis, we Þltered the data by deleting
records associated with campers or NRRS facilities in
Alaska, Hawaii, or Puerto Rico. We reasoned that it
would be unlikely for a visitor to transport Þrewood
betweentheselocationsandtheconterminousUnited
States. For the same reason, we also deleted records
from international visitors, except for visitors from
Canada; in their study of Þrewood surrendered at
MichiganÕs Mackinac Bridge, Haack et al. (2010)
noted multiple Þrewood-carrying vehicles from three
different Canadian provinces (Ontario, Alberta, and
Newfoundland and Labrador). Finally, we also re-
moved any records where the number of nights was
zero; these records indicated reservations for day use
rather than camping. After Þltering (that eliminated
?500,000 reservations), the data encompassed ?7.2
million individual reservations made at 2,525 camp-
grounds and related recreational facilities.
The NRRS supplied geographic coordinates for
these facilities, some of which USDA APHIS-PPQ
manually corrected after performing a spatial review
in a geographic information system. We also assigned
geographiccoordinatesforeachvisitorZIPcodeinthe
data set (or postal code for the Canadian visitor re-
cords) based on the centroids of the ZIP code poly-
gons (ESRI 2009b, Natural Resources Canada 2010).
Then, for each individual visitor reservation record in
thedataset,wecalculatedtheEuclidean(i.e.,straight
line) distance between the visitorÕs origin ZIP code
and the destination campground.
WeextractedsixsubsetsfromthefullNRRSdataset
for further analysis. Our main objective in analyzing
thesesubsetswastodeterminehowthedistributionof
travel distances for a particular subgroup of camp-
ground visitors might differ from the distribution for
all visitors. First, we separated the full NRRS data set
into four geographic subregions according to the lo-
cation of the destination campground cited in each
record:northeastern,southern,midwestern,andwest-
ern United States (Fig. 1). Second, to evaluate poten-
tial differences in the distance distribution for visitors
traveling to speciÞc popular destinations, we created
a subset of all records of visits to campgrounds within
50 km of the 20 most visited national parks in the
continental United States (National Park Service
[NPS] 2011). Third, to examine potential distribu-
tional differences for campground visitors from large
cities, we created a subset of all NRRS records orig-
Fig. 1.
the four analytical subregions.
Map showing the U.S. states comprising each of
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inating in the 20 most populous U.S. urban areas
(based on U.S. Census Bureau population estimates
and urban area boundary delineations).
KernelDensityEstimation.Forthefulldatasetand
each of the subsets, we developed an empirical esti-
mate of the probability density function of the travel
distance data using kernel density estimation. The
kernel density estimate provided a basic setting for
visually assessing the Þt of various theoretical distri-
bution functions to the data (see next section). For
this task, kernel density estimation avoids the discon-
tinuityofhistogramsthatarisesfrombinningthedata,
but has the potential disadvantage of smoothing out
some of the Þne-scale variation, particularly in long-
tailed distributions (Silverman 1986). A kernelÕs de-
gree of smoothing depends on a parameter, h, known
as the bandwidth; to determine h, we applied the
commonly used SilvermanÕs rule of thumb:
h ? 0.9An?1⁄5
[1]
whereAistheminimumofthestandarddeviationand
the interquartile range divided by 1.34, and n is the
sample size (Silverman 1986, Sheather 2004).
TheoreticalDistributionFitting.ForthefullNRRS
data set and each of the subsets, we Þtted the distri-
butionoftraveldistancesusinganumberofunivariate
theoreticaldistributionfunctions,manyofwhichhave
been used previously to depict dispersal kernels in
spatial invasion models (Kot et al. 1996, Lockwood et
al. 2007, Pitt et al. 2009). The distribution functions
thatweevaluatedwerethebeta,Cauchy,exponential
(i.e., negative exponential), gamma, lognormal, and
(two-parameter) Weibull distributions, as well as the
boundedandunboundedJohnsondistributions(often
denoted as the Johnson SBand SUdistributions, re-
spectively);notably,thelognormaldistributionisalso
considered part of the Johnson distribution family
(denoted in this context as Johnson SL). We Þt each
theoretical distribution function to the data via max-
imumlikelihoodestimationusingthefitdistrpluspack-
age in R (Delignette-Muller et al. 2010). For each
tested data set, we identiÞed the best-Þtting function
as the one with the lowest value of AkaikeÕs informa-
tion criterion, a commonly used metric for comparing
the goodness-of-Þt of models estimated by maximum
likelihood (Akaike 1973).
Mixture Distributions. An alternative to using a
univariate theoretical distribution function is to use a
“mixed-kernel” approach (Nathan et al. 2003), which
combine two or more functions that depict separate
aspects of dispersal. This sort of approach is a logical
extension of the aforementioned concept of stratiÞed
diffusion (i.e., where dispersal involves multiple pro-
cesses); for instance, a mixture distribution applied as
a dispersal kernel in a spatial model of an organismÕs
spread might integrate one theoretical distribution
function to represent short-distance dispersal via one
vector (e.g., the organismÕs own movement capabili-
ties) with a second function to depict rare long-dis-
tance dispersal via another vector, such as movement
of the organism by wind or as a “hitchhiker” on other
organisms(HigginsandRichardson1999,Higginsetal.
2003, Nathan et al. 2003). In actuality, even when an
organismÕs dispersal can be reasonably characterized
as single-vector, it is still likely to involve multiple
individualprocesses,eachassociatedwithaparticular
subpopulation or subgroup of the organism (Higgins
and Richardson 1999). We explored this premise with
the NRRS data, positing that, at least in some cases,
camper movement (representing one particular vec-
tor for dispersal of forest insects) might best be char-
acterized by a mixture of component distributions
correspondingtothebehaviorofcertainsocialgroups
of campers (e.g., weekend campers vs. vacationers
taking extended trips). Having identiÞed the best-
Þtting univariate theoretical distribution functions
(see previous section), we Þt mixtures of these the-
oretical distributions to the national parks and urban
areas subsets of the NRRS data. We did this using the
mixdist package in R (Macdonald 2010), which con-
tains tools for Þtting mixture distribution models to
grouped(i.e.,histogram)data.Althoughalackofdata
canmakeitdifÞculttoÞtmixtureswithmorethantwo
components, given the large sample size (N ?1.1 mil-
lion) of both the national parks and urban areas sub-
sets, we felt justiÞed in Þtting them with three- and
four-component mixture distributions. For each sub-
set,wejudgedthesuccessofthetestedmixturesbased
on the chi-squared approximation to the likelihood
ratio test as well as the standard errors of the compo-
nent distributionsÕ parameters (Macdonald 2010).
Results
Exploratory Geospatial Data Analysis. Figure 2
shows a map of the links between visitor origin ZIP
codesanddestinationcampgroundsforthefullNRRS
data set. The map suggests some basic trends in
camper travel behavior. First, the highest-volume
links (i.e., links with ?1,000 reservations, depicted in
red) are all ?250 km in length, and commonly much
shorter(?100km).Infact,mostlinkswithamoderate
(?50) to high volume of reservations are similarly
short in length. Although there are a few moderate-
volume links that exceed 1,000 km, the longest links
generally tend to be those associated with few (?25)
reservations. Regardless, instances of cross-country
travel by campground visitors are evident in the map,
asareasmallproportionofvisitsoriginatinginCanada
(mostprominentlyfromlocationsinAlberta,Ontario,
and Quebec).
Figure2alsodepictsanumberofdistinctclustersof
camper travel activity. For instance, CA contains
prominent clusters of travel from its major coastal
urban areas (i.e., San DiegoÐLos Angeles and San
FranciscoÐOakland) to campgrounds in the San Ber-
nardino or Sierra Nevada Mountains. Similar clusters
canbeseeninotherpartsofthewesternUnitedStates
(e.g.,fromtheDenver,CO,areaintotheRockyMoun-
tains), but the region with the highest overall level of
camper travel activity appears to be the southern
UnitedStates,particularlyintheareaextendingnorth
from eastern Texas to Missouri. The activity level in
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Page 5

this region may be somewhat visually exaggerated
becausethedestinationcampgroundsaremorewidely
dispersed geographically than in the western United
States. Nevertheless, close examination of the map
reveals a consistent pattern of high-volume travel in
this region, from both rural and urban locations to
destination campgrounds situated near major lakes
(or reservoirs) or National Forests.
Summary Statistics. For the continental United
States (i.e., the full NRRS data set), as well as the
southern, northeastern, and midwestern U.S. subre-
gions,themediantraveldistancewas?100km(Table
1). The median travel distance in the western United
States was somewhat higher (nearly 150 km). This
may be because destination campgrounds generally
tend to be further away from populated places in the
West,althoughthisresultwasprobablyalsoshapedby
characteristicsofthegeospatialdata;essentially,some
ZIP code areas in the western United States are quite
large, and because visitor travel distances are calcu-
lated from the centroids of ZIP code areas, these
distances are likely longer on average for this region
than for other parts of the United States. The median
traveldistancesforthenationalparksandurbanareas
subsets (Table 1) were even higher than for the west-
ern U.S. subregion, suggesting that particular target
destinations and places of origin do have at least a
marginal effect on camper travel behavior.
For all of the tested data sets, the average travel
distance was two to three times higher than the me-
dian distance, while the maximum travel distance was
?3,000 km (and ?5,500 km for the full data set and
some subsets). These high average and maximum
travel distance values relative to the median indicate
Fig. 2.
of individual visitor reservations recorded for a given link in the NRRS database. Links with 10 or fewer reservations have
been omitted.
Map of the links between visitor origin ZIP codes and destination campgrounds. Link color indicates the number
Table 1.
States) and all data subsets
Summary statistics describing the distributions of visitor travel distances for the full NRRS data set (i.e., continental United
Region/categoryN Avg. distance (SD) (km) Median distance (km)Max. distance (km)
Continental United States
Southern United States
Northeastern United States
Midwestern United States
Western United States
20 most visited national parks
20 most populous urban areas
7,220,563
3,140,537
358,584
1,338,091
2,383,351
1,144,999
1,117,898
235.8 (463.2)
175.0 (340.1)
180.4 (364.4)
170.4 (312.9)
360.9 (631.7)
488.7 (756.9)
370.7 (605.5)
92.6
67.7
85.3
78.4
148.3
213.4
171.6
5,565.9
5,565.9
4,531.6
3,279.5
5,435.9
5,435.9
4,538.7
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that the tested data sets are positively skewed, as
illustrated by the histogram for the full data set (Fig.
3). The histogram also shows the strongly leptokur-
tic nature of the data. For the full NRRS data set,
?10% of visitors traveled ?500 km, and ?5% trav-
eled ?1,000 km.
Theoretical Distribution Fitting. The inset plot in
Fig.3,whichisaclose-upupofthefulldatahistogram
at distances ?1,000 km, reveals something else signif-
icant: the peak density (i.e., the mode) of the distri-
bution of travel distances for the full data set is at a
distance of ?50 km. This implies that theoretical dis-
tributionfunctionssuchasthe(negative)exponential
or inverse power law, where the probability density
declines from a maximum at zero, are unlikely to
provide a good Þt to the data. Indeed, for the full data
set and all of the subsets, the best-Þtting theoretical
distribution function, based on minimum AkaikeÕs in-
formationcriterion,wastheunboundedJohnson(SU)
distribution, followed closely by the lognormal distri-
bution (i.e., another member of the Johnson distribu-
tion family). For the full data set, a plot of density as
estimated by the Johnson SUdistribution versus the
kernel density estimate (Fig. 4A) suggests a good Þt
across the entire range of travel distances; the only
apparent ßaw is under-prediction by the Johnson SU
at distances between 100 and 200 km (discernable in
the inset plot). However, a plot of the logarithm of
density versus distance (Fig. 4B), which more clearly
depicts differences between the kernel density esti-
mate and the Johnson SUat longer distances, reveals
over-predictionatdistancesbetween500kmand1,000
km and increasing under-prediction at distances
?1,000 km. (Note that the plot in Fig. 4B is truncated
Fig. 3.
up to 1,000 km.
Histogram of visitor travel distances based on the full NRRS data set. Inset plot shows the histogram for distances
Fig. 4.
estimate for the full NRRS data set. Inset plot shows distances up to 1,000 km; (B) plot of the logarithm of density versus
travel distance for the Johnson SUdistribution and the kernel density estimate for the full NRRS data set.
(A) Plot of density versus travel distance for the unbounded Johnson (SU) distribution and the kernel density
April 2012KOCH ET AL.: DISPERSAL OF INVASIVE FOREST INSECTS IN FIREWOOD
443

Page 7

atdistances?4,000km;beyondthisdistance,thenum-
berofobservationswasinsufÞcienttoderiveasmooth
logarithmic estimate of the kernel density.)
This pattern of Þt generally holds true for each of
the tested geographic subregions (Figs. 5 and 6) and
for the national parks and urban areas data subsets
(not shown). The kernel density estimates for the
northeastern United States and western U.S. subre-
gions (Fig. 5A, D, respectively) display a degree of
multimodality(i.e.,secondarypeaksatdistances?200
km) that is not well captured by the univariate John-
son SUdistribution, suggesting that mixture distribu-
tions might be more appropriate for these subsets.
Figure6showsaplotofthelogarithmofdensityversus
distance for each of the geographic subregions. (As
with the full NRRS data set, the logarithmic estimates
of the kernel density for each subregion become less
reliable as they approach the maximum recorded dis-
tance, which differed region-to-region; see Table 1.)
Thesubregionsexhibitunder-predictionatlongerdis-
Fig. 5.
andthekerneldensityestimate,basedondataforthefouranalyticalsubregions:(A)northeasternUnitedStates,(B)southern
United States, (C) midwestern United States, (D) western United States.
Plots of density versus travel distance (distances up to 1,000 km) for the unbounded Johnson (SU) distribution
Fig.6.
densityestimate,basedondataforthefouranalyticalsubregions:(A)northeasternUnitedStates,(B)southernUnitedStates,
(C) midwestern United States, (D) western United States. Distances ?4,000 km have been omitted.
PlotsofthelogarithmofdensityversustraveldistancefortheunboundedJohnson(SU)distributionandthekernel
444JOURNAL OF ECONOMIC ENTOMOLOGY
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tancesinamannersimilartothefulldataset,although
in the southern United States (Fig. 6B), under-pre-
diction begins at a comparatively shorter distance
(?750 km), and in the western United States (Fig.
6D), at a comparatively longer distance (?2,000 km).
MixtureDistributions.Figure7showsathree-com-
ponent lognormal mixture distribution applied to the
data subset for the 20 most visited U.S. national parks.
Table 2 shows the parameter estimates for each of the
component distributions. We used the lognormal be-
cause the Johnson SUis not implemented in the mix-
dist package (and the two performed similarly during
univariate distribution Þtting). The standard errors of
the parameter estimates were fairly low, suggesting
the estimates were precise, and the Þt of the mixture,
based on the chi-squared approximation of the like-
lihoodratio,washighlysigniÞcant(P?0.0001).How-
ever,theseÞndingsweresimilarlytrueofotherthree-
and four-component mixture distributions (as well as
single-component distributions) that we tested. In
short, there were a few reasonable candidate mixture
distributionsforthenationalparkssubset;weselected
theonethat,inourjudgment,appearedtoprovidethe
best overall Þt to the data histogram. In any case, a
Fig.7.
associated with the 20 most visited U.S. national parks. Inset plot shows distances up to 1,000 km. The individual component
distributions are depicted by red lines, while the red triangles indicate their mean (?) values.
Plotofathree-componentlognormalmixturedistribution(green)Þttedtothehistogram(blue)forthedatasubset
Fig.8.
associated with the 20 most populous U.S. urban areas. Inset plot shows distances up to 1,000 km. The individual component
distributions are depicted by red lines, while the red triangles indicate their mean (?) values.
Plotofafour-componentlognormalmixturedistribution(green)Þttedtothehistogram(blue)forthedatasubset
April 2012KOCH ET AL.: DISPERSAL OF INVASIVE FOREST INSECTS IN FIREWOOD
445

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noteworthy feature of the selected mixture is that the
third component distribution, which represents ?5%
ofthetotaldistribution(Table2),largelycapturesthe
longest distances in the national parks subset. Con-
versely, the other component distributions account
for very little of the density at these distances. This
supportsthepremisethatthedatareßectthebehavior
ofdistinctsubpopulationsoftravelers.Thus,thethree
component distributions may be interpreted as cor-
responding to three hypothetical groups of camp-
ground visitors: the large majority of overnight camp-
ers, whose travel times are typically less than a few
hours (component 1); campers visiting speciÞc des-
tination campgrounds (i.e., speciÞc national parks)
who are thus willing to travel farther (component 2);
and campers with longer-term itineraries, perhaps in-
volving the multiday use of recreational vehicles and
visits to multiple destinations (component 3).
Figure 8 shows a four-component lognormal mix-
ture distribution applied to the data subset for the 20
most populous U.S. urban areas, while Table 3 shows
the parameter estimates for each of the component
distributions. As with the mixture distribution for the
national parks data subset, the standard errors of the
parameter estimates were low, and the Þt was found
to be highly signiÞcant (P ? 0.0001). Also like the
national parks subset, other (three- and four-compo-
nent) mixture distributions that we tested performed
similarly in terms of these metrics, so we selected the
one that we judged to offer the best overall Þt to the
data histogram. One interesting aspect of the selected
mixture (and of the other candidate mixtures we
tested)isthepresenceoftwooverlappingcomponent
distributions (i.e., components 1 and 2). We hypoth-
esize that this resulted from the inherent structure of
the urban areas subset. Similar to component 1 in the
national parks subset, these components (that to-
gethercapturemostoftheshortdistancesrecordedin
the subset) likely correspond to overnight campers.
However, we suspect there is something of a split in
this subpopulation; basically, overnight campers from
certain densely populated, large cities (e.g., New
York) likely have to travel farther to get beyond de-
velopedareasthancampersfromcitiessurroundedby
a wide “transition zone” where wildlands and devel-
oped areas are highly intermixed. If we downplay this
difference and assume that components 1 and 2 rep-
resent slightly different portions of the same subpop-
ulation, then component 3 in the urban areas mixture
distributioncanbeinterpretedsimilarlytocomponent
2 in the national parks mixture (i.e., representing
campers visiting speciÞc destinations and thus willing
to travel farther), while component 4 can be inter-
preted similarly to component 3 in the national parks
mixture (i.e., representing campers with longer-term
itineraries).
Discussion
The analyses presented in this study lead to two
major generalizations. The Þrst generalization is that
a majority of campground visits involve relatively
short travel distances (?100 km, which is usually a
?2-hdrivefromhome).Thisisnotsurprising,because
most campground visits probably last only a few days
(e.g., a weekend), and under such circumstances,
campersarelikelytominimizethetraveltimetotheir
destinations. Nevertheless, given that some percent-
age of campers are likely to carry infested Þrewood,
these short-distance trips are highly relevant in an
invasion context, because they have the potential to
transport forest insect pests well beyond their natural
dispersal range. For example, in ßight mill studies, the
medianßightdistanceofA.planipennismatedfemales
was?3kmin24h(withonly1%ßying?20km),while
massmark-recapturestudiesofA.glabripennissuggest
anaturaldispersalpotentialof2Ð3kmperyear(Smith
et al. 2001, 2004; Taylor et al. 2010). Furthermore,
based on the NRRS data, the percentage of camp-
ground visits involving longer travel distances (i.e.,
?500 km) appears to be substantial (10% in the full
data set).
The second major point is that we were able to
attain a good Þt with theoretical distribution func-
tions, despite the data being strongly leptokurtic. A
primary reason for this success was that the NRRS
database and its subsets had large sample sizes and
were temporally robust (i.e., spanning a 5.75-yr pe-
riod), thus providing adequate data to reasonably
characterize the likelihood of long-distance dispersal
events. Nevertheless, the observed Þts with the John-
son SUdistribution, which was the best-performing
univariate function in all cases, were not perfect. In
particular, the Johnson SUdistribution consistently
under-predicted dispersal likelihood at very long
(?1,000 km) travel distances. This is not necessarily
problematic for modeling dispersal of forest insect
pests in Þrewood, because the region of under-pre-
diction generally encompassed only the rarest long-
Table 2.
distributions of a lognormal mixture applied to the data subset for
the top 20 most visited U.S. national parks
Parameter estimates (?SE) for the three component
Component
? (SE)
? (SE)
? (SE)
1
2
3
0.735 (0.012)
0.211 (0.012)
0.054 (0.000)
270.7 (3.685)
624.9 (10.685)
2,990.4 (3.979)
412.0 (7.092)
707.5 (7.01)
587.4 (3.207)
The parameter ? represents the proportional contribution of each
componenttotheoverallmixturedistribution,?isthemean(distance
in kilometers) of each component, and ? is its standard deviation.
Table 3.
distributions of a lognormal mixture applied to the data subset for
the top 20 most populous U.S. urban areas
Parameter estimates (?SE) for the four component
Component
? (SE)
? (SE)
? (SE)
1
2
3
4
0.218 (0.005)
0.231 (0.007)
0.481 (0.011)
0.070 (0.001)
89.6 (4.076)
124.4 (0.511)
348.1 (2.745)
2,211.6 (10.788)
142.7 (9.387)
46.0 (0.664)
263.2 (2.893)
1,037.9 (4.738)
The parameter ? represents the proportional contribution of each
componenttotheoverallmixturedistribution,?isthemean(distance
in kilometers) of each component, and ? is its standard deviation.
446JOURNAL OF ECONOMIC ENTOMOLOGY
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distance events (?1Ð2% of the observed distances),
and campers who travel such long distances may be
lesslikelytobringÞrewoodwiththem.Regardless,the
superiority of the Johnson SUdistribution (and log-
normal distribution) to the other theoretical distribu-
tion functions we tested suggests that invasion mod-
elers should carefully consider their assumptions
regarding what distribution will provide the best ker-
nel for modeling a long-distance dispersal process
(i.e., commonly used distributions like the negative
exponential may not always be appropriate).
The kernel density estimates for two of our geo-
graphic subregions displayed some degree of multi-
modality. Based on our Þtting of mixture distributions
to the national parks and urban areas subsets, it seems
likely that we could also successfully Þt mixtures to
thesesubregionaldatasets.Mixturedistributionshave
the additional advantage of dividing the data into dif-
ferentsubpopulations,which,forexample,couldeach
beassignedauniqueprobabilityoftransportingforest
insects.Thenotionofsubpopulationsofcamperswith
distinctive travel patterns also has important implica-
tions for developing public awareness campaigns and
outreach programs. For example, each subpopulation
could be targeted with an individual suite of policies,
which might prove more efÞcient than applying a
“blanket” approach to all campers.
Two important limitations of our analysis should be
mentioned.First,becauseofprivacyconcerns,allper-
sonallyidentiÞableinformationwasremovedfromthe
NRRS data records before their release to us. As a
result, we were unable to document cases where a
camper made reservations at several different camp-
grounds on consecutive or near-consecutive dates
(i.e., a multi-stop itinerary). In truth, some of the
longer-distance campground visits that we portrayed
as“nonstop”tripsinouranalysislikelyinvolvedoneor
more intermediate stops along the way. It seems un-
likely that the campers on these multi-stop trips who
began traveling with Þrewood brought from home
were still carrying it when they reached their Þnal
destinations. However, it is also quite plausible that
theykeptsomeÞrewoodfromapreviousstop,possible
hundredsofkilometersaway.Ineffect,thesecampers
still presented a substantial risk of introducing forest
insect pests to novel locations. Ultimately, we made
the simplifying assumption that the potential effect of
multi-stopcamperitinerariesonthedispersaldistance
estimates was mitigated by a presumably much larger
proportionofsingle-stopitinerariesintheNRRSdata,
as well as by scenarios such as the one just described.
A second limitation relates to our use of Euclidean
distanceasthemeasureofthetraveldistancebetween
each visitor origin ZIP code and destination camp-
ground. A more realistic distance measure would be
thelengthofthemostlikelyroadrouteconnectingthe
two locations. Unfortunately, determining the most
likelyrouteforeachorigin-destinationcombinationis
a difÞcult computational problem, made even more
challengingbythelargevolumeofsuchcombinations
intheNRRSdata.Foremost,themostlikelyroadroute
is not necessarily the shortest-length route; for exam-
ple, various categories of roads (e.g., interstate high-
ways vs. local access roads) may permit dramatically
different travel speeds, thus inßuencing travelersÕ
route choices. Although the Euclidean distance be-
tween two geographic locations underestimates the
route-based travel distance by some unknown
amount, the sophisticated geospatial modeling efforts
necessary to determine the latter for each unique
origin-destinationcombinationintheNRRSdatawere
beyond the scope of this analysis. However, this is a
key area for future work.
Acknowledgingtheselimitations,ourstudyhasnev-
ertheless presented a straightforward quantitative ap-
proach for developing and parameterizing dispersal
kernels to characterize the spread of forest insects via
recreational travel. Additionally, we have shown that
the kernels, whether based on univariate or mixture
distributions, can be customized for certain invasion
scenarios and geographic subsets (e.g., analyzing the
expansion of an insect pest in a particular region of
interest, or focusing on campgrounds with environ-
mental conditions especially suitable for an invader).
We envision one of these kernels (or a similarly de-
rivedkernel)beingusedtosimulaterecreational(i.e.,
camper-related) dispersal in spatial invasion models,
as a complement to algorithms depicting biological
dispersal or other modes of human-mediated disper-
sal. To do so would require making assumptions re-
garding the propagule pressure (i.e., number of dis-
persing individuals; Lockwood et al. 2005) associated
with the kernel; regrettably, with respect to recre-
ationally transported Þrewood, the existing data are
insufÞcient in quantity and geographic scope to make
anything but coarse propagule pressure estimates for
individual forest pests of interest. (In fact, a lack of
empirical data about propagule pressure is a universal
problem for invasion modeling; see Lockwood et al.
2007.)
Still, we can use the available information on Þre-
wood to make some general statements regarding the
risk of spreading forest insects in the United States.
Based on data compiled from a small number of Þre-
woodinspectionsandusagesurveys(Haacketal.2010,
USDA-APHIS 2011b), we estimate that 30Ð40% of
campers carry Þrewood from home (or other distant
locations). If we assume that ?20% of the Þrewood is
infested with live wood borers (roughly equal to the
percentage reported by Haack et al. 2010), then ?6Ð
10% of campground visits involve the movement of
Þrewood infested with viable forest insects. Account-
ing for factors such as the burning of Þrewood before
anypestscanescape,orthefactthatsometransported
insectspecieswillalreadybepresentattheireventual
destinations,itseemsreasonabletoestimatethat3Ð5%
ofcampgroundvisitsposeapotentialriskofÞrewood-
mediated dispersal of forest pests. The NRRS data
used in this study recorded an average of ?1.2 million
campground visits per year. Furthermore, these data
represent only a subset of all campground visits in the
United States; for instance, there are ?9,000 private
campgrounds distributed across the country, com-
paredwith2,525fortheNRRS(USDA-APHIS2011b).
April 2012KOCH ET AL.: DISPERSAL OF INVASIVE FOREST INSECTS IN FIREWOOD
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This implies that, even if only 1% of recreational Þre-
wood contained viable insects, potentially tens of
thousands of camping trips occur each year in the
UnitedStatesduringwhichinfestedÞrewoodistrans-
ported to a distant location. Hence, current concerns
about the risk of forest pest spread in camper-trans-
ported Þrewood appear to be well justiÞed.
Infact,abetterquestionmightbewhywehavenot
seen a greater proliferation of forest insect pests be-
cause of recreational Þrewood transport. We believe
there are a few feasible explanations for this. Most
likely, the environmental conditions or the reproduc-
tive capacity of the introduced insects, especially
giventhepotentialforAlleeeffects(TaylorandHast-
ings2005),areinadequateforestablishmentinthevast
majority of Þrewood-related introductions. The in-
sectsÕ speciÞc life history attributes may also affect
establishment likelihood. For instance, Haack et al.
(2011)notedsubstantialvariationintheratesatwhich
different forest insect families infest host material.
Theyestimatedthataninfestedlog?1minlengthand
?10 cm in diameter could be expected to contain
100Ð250 individual bark beetles, 20Ð30 buprestids
(e.g., A. planipennis), or 5Ð10 cerambycids (e.g., A.
glabripennis).Theseestimatessuggestthatabundleof
infested Þrewood is more likely to contain a sufÞcient
population of bark beetles for establishment than a
sufÞcient population of larger borers (such as bupres-
tids or cerambycids). Alongside such population-
based explanations, it is possible that the existing reg-
ulations and public awareness campaigns are indeed
having a positive effect on human behavior with re-
spect to Þrewood use and transport. Alternatively, it
may be the case that many existing infestations initi-
ated by Þrewood have simply not been detected yet.
The correct answer is probably some combination of
these possibilities.
The spread of invasive pests via recreational travel
(and associated Þrewood transport) is conceptually
similar to other modes of human-mediated dispersal,
suchasthemovementofinvasiveorganismswithtrad-
able commodities (Hulme et al. 2008). However, cer-
tainaspectsofrecreationaltravelaredistinctive,sothe
dispersal patterns (i.e., dispersal kernels) observed in
this study may not translate directly to other human-
mediated dispersal processes. For example, with re-
spect to domestic trade, commodities are generally
moved along pathways linking areas of high industrial
or agricultural activity to populated places (i.e., cities
and towns). In contrast, recreational travel follows
pathways that link populated places to destinations
that are often located in sparsely populated regions.
Thus, the destinations and underlying objectives of
these two potential human-mediated dispersal modes
are quite different. Notably, residential Þrewood us-
age, which we did not consider in this study, involves
aspectsofbothmodes:Manyhomeownersobtaintheir
Þrewood directly from private (e.g., individually
owned woodlots) or public lands (e.g., through fuel-
wood harvesting permits on National Forests), while
others purchase it from large retail or wholesale dis-
tributors (USDA-APHIS 2011b). Given that Þrewood
is used regularly in ?30 million U.S. homes (Houck et
al. 1998), this topic probably deserves further analyt-
ical attention from a biological invasions perspective.
A Þnal, technical point pertains to the appropriate
application setting for the dispersal kernels presented
in this study. The kernels are effectively omni-direc-
tional; in other words, the likelihood of dispersal from
a given point of origin to a given destination is simply
a matter of the distance, and not the orientation, be-
tween the two points. While omni-directional kernels
may be satisfactory for many spatial modeling appli-
cations, it may be more realistic to use the NRRS data
inanetwork-basedsetting,wheredispersaloccursvia
speciÞedroutes(e.g.,roadcorridors)andisrestricted
to the set of potential destinations (e.g., camp-
grounds) deÞned for the network. Additionally, the
networked data could also serve as the basis for a
pathway model, which could provide, for example,
probabilisticestimatesofthemostlikelypathwaysand
destinations for a forest pest introduced at a given
origin node. Network-based implementation of the
kernels derived in this study will be a focus of future
research.
Insummary,ouranalysesappeartovalidatecurrent
regulatory and public outreach efforts regarding Þre-
wood transport and the potential spread of invasive
forest pests. Although most campers travel relatively
short distances, and even though only a small propor-
tionofthesecampersarelikelytobecarryinginfested
Þrewood,thisstilltranslatesintoasizeableincreasein
dispersal potential beyond the natural spread capa-
bilities of most forest insects. This is especially true
given the huge number of camping trips that occur
each year. While many aspects of the Þrewood issue
remain unclear, we have provided some preliminary
answers that should prove useful to decision makers
and other researchers. Additional work is needed to
relate our Þndings to the unique circumstances of
individual species of interest.
Acknowledgments
We thank Judith Pasek, David Kowalski, and Daniel
Borchert (USDA-APHIS) for providing the data used in this
study.WealsothankKurtRiittersandJohnCoulston(USDA
Forest Service), as well as two anonymous reviewers, for
their helpful comments. Frank KochÕs initial work on the
study was supported by Research Joint Venture Agreement
10-JV-11330146-064 between the U.S. Department of Agri-
culture, Forest Service, Southern Research Station, Ashe-
ville, NC, and North Carolina State University.
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Received 12 August 2011; accepted 7 December 2011.
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