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Applied Geography 40 (2013) 161e170

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Applied Geography

journal homepage: www.elsevier .com/locate/apgeog

A GIS-based risk rating of forest insect outbreaks using aerial overviewsurveys and the local Moran’s I statistic

Christopher Bone a,*, Michael A. Wulder b, Joanne C. White b, Colin Robertson c,Trisalyn A. Nelson d

aDepartment of Geography, University of Oregon, PO Box 1251, Eugene, OR 97403, USAbCanadian Forest Service (Pacific Forestry Centre), Natural Resources Canada, 506 West Burnside, Victoria, BC V8Z 1M5, CanadacDepartment of Geography & Environmental Studies, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canadad Spatial Pattern Analysis & Research (SPAR) Laboratory, Department of Geography, University of Victoria, PO Box 3060, Victoria, BC V8W 3R4, Canada

Keywords:Local indicators of spatial associationMoran’s IiAerial overview surveysMountain pine beetleInsect outbreaks

* Corresponding author. Tel.: þ1 541 346 4197.E-mail address: cbone@uoregon.edu (C. Bone).

0143-6228/$ e see front matter � 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.apgeog.2013.02.011

a b s t r a c t

The objective of this study is to provide an approach for assessing the short-term risk of mountain pinebeetle Dendroctonus ponderosae Hopkins (Coleoptera: Scolytidae) attack over large forested areas basedon the spatial-temporal behavior of beetle spread. This is accomplished by integrating GIS, aerial over-view surveys, and local indicators of spatial association (LISA) in order to measure the spatial relation-ships of mountain pine beetle impacts from one year to the next. Specifically, we implement a LISAmethod called the bivariate local Moran’s Ii to estimate the risk of mountain pine beetle attack across thepine distribution of British Columbia, Canada. The bivariate local Moran’s Ii provides a means for clas-sifying locations into separate qualitative risk categories that describe insect population dynamics fromone year to the next, revealing where mountain pine beetle populations are most likely to increase, stayconstant, or decline. The accuracy of the model’s prediction of qualitative risk was higher in initial yearsand lower in later years of the study, ranging from 91% in 2002 to 72% in 2006. The risk rating can becontinually updated by utilizing annual overview surveys, thus ensuring that risk prediction remainsrelatively high in the short-term. Such information can equip forest managers with the ability to allocatemitigation resources for responding to insect epidemics over very large areas.

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Introduction

The mountain pine beetle, Dendroctonus ponderosae Hopkins(Coleoptera: Scolytidae) is the most destructive insect pest of pineforests in western North America (Safranyik, 1988). Since 1999, theinsect has affected more than 16 million ha of pine forests inwestern Canada (Westfall & Ebata, 2010). The current epidemic,largely located in British Columbia, has resulted in substantialcommercial timber loss (Pederson, 2004), increase risk to fire andhabitat loss (Coops, Waring, Wulder, & White, 2009; Jenkins,Herbertson, Page, & Jorgensen, 2008), and alterations to carboncycling processes (Coops & Wulder, 2010; Kurz et al., 2008; Pfeifer,Hicke, & Meddens, 2011). In addition, there is concern that thebeetle will infest further beyond its historical range (Sambarajuet al., 2011) as warmer seasonal temperatures exacerbate theoutbreak and permit it to move to higher latitudes and elevationsthan previously recorded (Logan, Régnière, & Powell, 2003), and

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across the geoclimate divide as defined by the Rocky Mountainrange of North America (Safranyik et al., 2010). Such concernsindicate a need for risk analyses that can inform forest manage-ment decision making over vast areas in a timely manner.

In British Columbia, the mountain pine beetle mostly attackslodgepole pine (Pinus contorta) (Flint, McFarlane, & Muller, 2009).The process begins in the summer as beetles emerge from theirhost and spend time in flight searching for a new tree to attack.Once located, the beetle attempts to bore through the bark andrelease pheromone chemicals to attract additional beetles to thesuitable host (Powell et al., 2000). After boring through the phloemof the tree, beetles copulate and proceed to dig galleries that areused to oviposit (Raffa et al., 2008). As beetles bore through thebark, they inoculate the tree with two types of blue stain fungi thatrapidly penetrate living tree cells, thereby impacting the capacityfor translocation of moisture and nutrients through the tree,consequentially limiting the ability of the tree ward off attack(Paine, Raffa, & Harrington, 1997; Six & Paine, 1998). The combi-nation of pheromone release and fungi inoculation facilitates amass attack of beetles on an individual tree that are needed toovercome a tree’s defensive mechanisms (Safranyik, 2004).

Fig. 1. Number of hectares impacted by mountain pine beetle from 1999 to 2011.

C. Bone et al. / Applied Geography 40 (2013) 161e170162

Reproduction ensues in the weeks following tree mortality, andyoung beetles then overwinter under the bark and then emerge inthe following summer to repeat the same process.

Individual trees vary in their susceptibility to attack as beetleshave preference for trees that provide ample resources for repro-duction and growth while also providing minimal resistance toattack (Berryman, 1978). Trees with larger diameters, for example,receive relatively higher densities of attack because the rougherbark associated with larger trees is preferred for initiating galleries(Safranyik, 1971), and the thicker phloem provides protection frompredators and extreme temperatures (Reid, 1963), thus increasingthe likelihood of progeny survival. Beetles also prefer older trees,generally over 80 years of age, because their vigor diminishes as ageincreases (Safranyik, 2004). In addition, dense stands of older treesare preferred as increased competition for resources comprise theirability to resist attack (Mitchell, Waring, & Pitman, 1983).

Identifying forest stands at risk to mountain pine beetle attackaids in the mitigation and prevention of outbreaks. The term risk inthe bark beetle literature has come to refer to “the short-term ex-pectancy of tree mortality in a stand as a result of mountain pinebeetle infestation” (Shore, Safranyik, & Lemieux, 2000, p.44), withrisk being a function of both stand susceptibility (i.e., the ability of astand to support a beetle population) and the magnitude of sur-rounding mountain pine beetle populations e often referred to aspopulation pressure (Bentz, Amman, & Logan, 1993).

When beetle infestations expand over large areas as hasoccurred with the current outbreak, estimating risk becomes acomplicated task because of the data required for calculating sus-ceptibility. Risk models with a susceptibility component (Amman,McGregor, Cahill, & Klein, 1978; Berryman, 1978; Mahoney, 1978;Schenk, Mahoney, Moore, & Adams, 1980; Shore & Safranyik, 1992)rely upon data that provide details concerning, for example,average tree age, tree diameter, phloem thickness, basal area,crown competition and stand growth. Such data can be collectedand analyzed in a timely manner when infestations remain rela-tively small. However, large outbreaks require that risk models beapplied over large areas, which means that models must then relyupon regional inventory records to provide the necessary data(Robertson, Wulder, Nelson, & White, 2008). For example, theBritish Columbia Ministry of Forests, Lands and Natural ResourceOperations provides the Vegetation Resources Inventory (VRI),which is a two-phased vegetation inventory with attributes esti-mates through a combination of aerial photo interpretation andground sampling (BCMSRM, 2002). The utility of such inventoriesbecomes increasingly limited when bark beetle outbreaks causechanges to forest composition (via beetle-induced tree mortality orharvesting-based mitigation efforts) occur far more swiftly thaninventory updates. This is especially true in British Columbiawherethe current mountain pine beetle outbreak has grown swiftly since2000 (see Fig. 1).

In contrast to the data needs associated with estimating sus-ceptibility under large-area mountain pine beetle outbreak sce-narios, estimating population pressure under similar scenarios canbe accomplished through the use of a single dataset: forest healthaerial overview survey (AOS) data. In British Columbia, AOS areannual, systematic surveys of a broad range of forest health issues.Designed to cover the largest possible area, the AOS are conductedby trained practitioners in fixed-wing aircraft, who provide esti-mates of beetle-induced tree mortality and other forest healthinformation (Wulder, White, Bentz, & Ebata, 2006). The AOS is astrategic-level data source that is rapidly disseminated to the public(i.e., within 3 months of survey completion) (Wulder et al., 2009),and that can serve as a surrogate for beetle population pressure.Furthermore, because the AOS are conducted annually, changes inpopulation pressure can be estimated across a region, which is

important for determining if populations are increasing ordecreasing in specific areas in order to prioritize mitigation efforts.

While focusing risk estimates solely on population pressure isonly part of the risk equation, we posit that data on regional pop-ulation dynamics collected from AOS can aid in identifying andprioritizing areas of imminent risk to mountain pine beetle in-festations over large areas. As such, this study proposes a GIS-basedrisk rating system of mountain pine beetle infestations by inte-grating multi-year AOS data and local indicators of spatial associ-ation (LISA) (Anselin, 1995) for estimating infestation risk at aregional scale. We extend previous applications of LISA for esti-matingmountain pine beetle infestations (Nelson & Boots, 2008) byapplying the bivariate local Moran’s Ii to determine local spatialrelationships in beetle infestations in subsequent years. Theobjective of developing a regional risk rating system based onsurrogate measures of population pressure across multiple years isto inform management of where lies increasing, constant ordeclining risk. As mountain pine beetle population dynamics arecontrolled by numerous local and regional processes that interactwith each other over time, it is difficult to project where pop-ulations will arrive, increase or diminish from one year to the nextover a region without examining the spatial and temporal distri-butions of populations. We anticipate that this regional risk ratingsystemwill be able to be used in unisonwithmore localized data onsusceptibility characteristics in order to provide a more effectivemeans of mitigating outbreaks.

Methods

Study site and data

The study site (see Fig. 2) is defined by the distribution oflodgepole pine in British Columbia, which is an area coveringapproximately 30 million hectares of the provinces’ 95 millionhectare land mass (BC Ministry of Forests, 2004). The pine distri-bution data exists as a 1 km resolution raster grid inwhich each cellis represented by the estimated percentage of pine at that location.The dataset was developed by Robertson et al. (2009) to supportestimates of the compositional change of pine forests in BritishColumbia due to mountain beetle attack.

The severity of mountain pine beetle attack, which refers to thepercentage of trees successfully attacked within a given area(Wulder et al., 2006), was used as a proxy for beetle populationlevels. Severity informationwas acquired from annual forest healthaerial overview surveys (AOSs) (http://www.for.gov.bc.ca/hfp/health/overview/overview.htm), which are conducted province-wide by trained observers in fixed-wing aircraft. These AOS arecompleted quickly and efficiently, making them ideally suited for

Fig. 2. Study site (pine distribution) and the extent of the mountain pine beetleinfestation as of 2006.

C. Bone et al. / Applied Geography 40 (2013) 161e170 163

mapping the general location, gross area, and general trend (i.e.,increasing, decreasing, or stable) in damage caused by mountainpine beetle over large areas. Damage is observed and recorded onbasemaps with scales of either 1:100,000 or 1:125,000, and aseverity class (i.e., trace, light, moderate, severe, or very severe) isassigned according to the proportion of pine trees that are killed bythe beetle (Table 1). The limitations of these survey data includelarge errors of omission when damage is very light and a lack ofrigorous positional accuracy. The surveys were analyzed byWulderet al. (2009) in order to develop spatial datasets representingseverity values across the province at the 1 ha scale. For this study,the data were aggregated to a 1 km scale in order to agree with theresolution of the pine distribution data.

Predicting risk classes

LISA represents a set of localized statistical approaches thattypically measure the relationship between individual locationsand their surrounding neighbors to uncover patterns of spatialclustering. For this study, we employ the local Moran’s Ii, adecomposition of the global Moran’s Ii, for quantifying spatialautocorrelation. While the global statistic provides an overallmeasure of spatial autocorrelation, the local Moran’s Ii relates eachobservation to its neighbors and assigns them to classes with avalue indicating the degree of spatial autocorrelation. The localMoran’s Ii estimates the similarity in x between observation i andobservations j in the neighborhood of i defined by a matrix of

Table 1Severity class as defined by the percentage of area infested by mountain pine beetle.Table also provides information on the total area infested in each class for the years2000 (Westfall & Ebata, 2001) and 2006 (Westfall & Ebata, 2007). Note that the verysevere and trace classes were added in 2004. However, the trace class is omittedhere as no area in the study site was allocated to this class.

Severity class Area infested (%) Area infested in2000 (ha)

Area infestedin 2006 (ha)

Light 1e10 77, 746 2,933,172Moderate 11e30 92, 554 2,933,172Severe 31e49 114, 889 1,230,869Very severe �50 n/a 516,894

weightswij. The strength of the relationship between the neighborsis accordingly captured. The statistic, provided by Anselin (1995), iscalculated as:

Ii ¼

266664

zi0B@

Piz2i

n

1CA

377775Xj

wijzj (1)

where.zi ¼ xi � x:In essence, Eq. (1) standardizes value x for observation i to

determine if it is high or low relative to the mean, and standardizesvalues of x for j to determine if the neighborhood is high or lowrelative to the mean. The standardization operates in a similarmanner as a statistical z-score that compares observations to themean in order to determine the observations’ relative positionwithin a distribution. In the absence of such standardization, theresulting Moran’s Ii values would be disproportionately influencedby extreme values of severity. Multiplying the standardized value xfor observation i and the neighborhood j produces a scalar Moran’sIi value; these values can conceptually be placed into one of fourcategories representing the relationship between each point and itsneighbors: (1) LoweLow, (2) HigheLow, (3) LoweHigh, and (4)HigheHigh. The results from the local Moran’s Ii operation can bevisualized in aMoran’s scatterplot that displays the location of eachobservation within the solution space of its assigned class. Withinthe scatterplot, the local Moran’s Ii value describes the relativelocation of observation iwithin the two-dimensional solution spaceof each category. Note that not all Moran’s Ii values are significant: atest of significance is computed for each point to determine if thespatial relationship is significant given a specified level of confi-dence. Thus, just because a Moran’s Ii value provides a means forclassifying a data point’s spatial relationship with its neighbors, itdoes not guarantee that this relationship is significant. For furtherreading on the parameterization and utility of both the global andlocal Moran’s Ii, please see Tiefelsdorf and Boots (1995), Waldhor(1996), and Zhang, Luo, Xu, and Ledwith (2008).

An extension of this method is the bivariate local Moran’s Ii inwhich variable x of observation i is compared to variable y of theneighborhood j. The modified equation from for bivariate localMoran’s Ii takes the form:

Ii ¼

266664

zi0B@

Piz2i

n

1CA

377775Xj

wij

�yj � y

�(2)

The bivariate Moran’s Ii facilitates the examination of multi-temporal data relating to mountain pine beetle severity. Theseverity at a location from two years prior to the present (year t� 2)can be compared to the severity in its neighborhood at year t � 1 todetermine the spatial and temporal patterns of beetle spread attime t. Examining the relationship between tree mortality at alocation in a specific year versus treemortality in the neighborhoodin a subsequent year results in a severity rating that incorporateschange; in the absence of the temporal component of our analysiswe would be ignoring the potential that mountain pine beetlepopulations are increasing or decreasing in an area. For example,severity in 2000 at a specific location is compared to severity in itsneighborhood in 2001. The resulting estimated bivariate localMoran’s Ii class, (referred to hereafter as risk class) is then used torepresent risk for that location in 2002. This is repeated for each

C. Bone et al. / Applied Geography 40 (2013) 161e170164

year in order to retrieve the risk classes for the period between2002 and 2006. Eq. (2) thus becomes

Ii ¼

266664

zi;t�20B@

Piz2i;t�2

n

1CA

377775Xj

wijzj;t�1 (3)

where Ii,t is the Moran’s Ii for location i at time t,zj;t�1 ¼ xj;t�1 � xj;t�1, and zi;t�2 ¼ xi;t�2 � xi;t�2.

The Moran’s Ii identifies spatial autocorrelation in valuesextreme relative to mean values and subsequently facilitates theclassification of locations into risk classes. A Moran’s Ii scatterplotprovides a depiction of how each observation can be categorizedbased on its relationship with its neighbors. The scatterplot’s x-axisdefines the value of observation i relative to the mean of all ob-servations, while the y-axis defines the value of observations in theneighborhood of i relative to the mean of all observations. Thescatterplot consists of four quadrats, each defining the relationshipbetween an observation and its neighbors. Fig. 3 depicts aMoran’s Iiscatterplot in the context of this study. Class 1 (LoweLow) repre-sents an observation i that experiences zero to minimal severity attime t � 2 and whose neighborhood experiences zero to minimalseverity at time t � 1. Therefore, we expect that observations inclass 1 will not experience a significant increase in severity andhence have zero to minimal severity at time t. We term this the Nullclass as we do not expect large magnitude infestations in the im-mediate future. Locations in the Null class exhibit positive Moran’sIi values (the larger value the greater the difference in severitybetween the location and the mean neighborhood severity) inconcert with low severity.

Observations in class 2 (HigheLow) experienced greater thanaverage severity at time t � 2 and below average severity in theneighborhood at time t � 1. These locations exhibit negative Mor-an’s Ii values as the relationship between a location and its neigh-borhood is governed by negative spatial autocorrelation. Thus, we

Fig. 3. A conceptual schematic of the Moran’s Ii scatterplot. Arrows within each classrepresents the direction of Moran’s I values from 0 to 1. Each quadrat represents therelationship between observation i and its neighborhood. In addition, each quadratrepresents a different class of mountain pine beetle risk.

expect that the severity at t should be declining toward low tomoderate severity because there exists a diminished attack severityin the neighborhood of i in the subsequent year. This class isreferred to as the Decline class as it represents areas where in-festations are expected to diminish.

Observations in class 3 (LoweHigh) are also defined by anegative spatial autocorrelation relationship as the locationsexperienced low severity at t � 2 but above average severity in theneighborhood at t � 1. Therefore, severity should be increasinghighest amongst all classes toward moderate to high severitybecause there exists greater insect population pressure in theneighborhood in the subsequent year. We refer to this class as theIncrease class because such locations are experiencing a growth inthe infestation.

Observations in class 4 (HigheHigh) experienced higher thanaverage severity at t � 2 and higher than average severity in theneighborhood at t � 1; this class, which exhibits positive Moran’s Iivalues, is thus defined as the Constant class. Our expectation forseverity in class 4 depends on length of time a location has been inthe class. For locations that enter class 4, we expect that severitywill increase as heightened population levels attack stands ofvarying susceptibility. For locations in class 4 for multiple years, weexpect severity to decline due to the diminishing availability ofsusceptible hosts.

The neighborhood in the local Moran’s Ii should be represen-tative of the distance over which a location exhibits a relationshipwith its surrounding area. With regards to mountain pine beetledispersal, this task entails defining a neighborhood based on thedistance that the insect typically fly during their summer dispersalperiod. We estimated a measure of insect dispersal by examiningthe nearest neighbor distance between cells that exhibited attack ina specific year and cells that exhibited attack for the first time in thesubsequent year. This measure represents our best estimate atdetermining the least distance that mountain pine beetle dispersesfrom one year to the next. The bivariate local Moran’s Ii wascomputed using the software program GeoDa (Anselin, Syabri, &Kho, 1996) e a GIS-based application focused on estimating localand global spatial relationships in attributes represented in GISdata.

Risk rating evaluation

The use of the bivariate local Moran’s Ii to assign a risk class wasfirst assessed by performing a cell-by-cell comparison between ourestimated risk classes against observed severity classes in ArcGIS 10(Esri, 2011). The severity classes were defined using the Govern-ment of British Columbia’s severity rating system shown in Table 1,which also include the total area in the province within each classin 2006. The Moran’s Ii is considered to be correct if:

1. A cell assigned to the Null risk class at time t represents alocation that belongs to the None severity class at time t.

2. A cell assigned to the Increase risk class represents a locationthat experienced an increase from one severity class to another(e.g. from light to moderate).

3. A cell assigned to the Constant risk class represents a locationthat (a) did not experience a change in severity classes and (b)is not in the None severity class.

4. A cell assigned to the Decline risk class represents a locationthat experienced a decline from one severity class to another(e.g. from moderate to light).

The relationship between estimated and observed severity wasalso examined in a graphical context to determine if and how theMoran’s Ii either over- or underestimated severity.

C. Bone et al. / Applied Geography 40 (2013) 161e170 165

Next, we examined the distribution of risk classes with regardsto our expectations (described in Section 2.2) of how the classesshould represent spread. During early years of the infestation, theConstant class should constitute the nucleus of the infestation, theIncrease class will exist in the frontier of the infestation, and theNull class will compose the remainder of the landscape wherebeetle-induced tree mortality is absent. As the infestation increasesover time, the cluster pattern remains the same with the exceptionof the Decline class emerging in the center of the infestation. TheDecline class represents locations where host trees becomeexhausted and mountain pine beetle populations move ontoalternative locations.

Results

Estimating neighborhood size

The appropriate neighborhood size for the local Moran’s Ii sta-tistic was estimated from the nearest neighbor calculations per-formed in ArcGIS 10 (Esri, 2011) between the datasets representingsuccessive years of attack. The results from the nearest neighboranalysis are presented in Fig. 4. The frequency distributionsrepresent the minimal distance over which mountain pine beetledispersed in order to attack trees located in a cell that had yet toexperience attack. The majority of dispersal occurs within a dis-tance of 3 km, while longer-range dispersal is observed at varyingdistances from one year to the next. We thus selected 3 km as ourneighborhood size for the local Moran’s Ii statistic, which is sup-ported by previous research (Safranyik, 1989; Shore & Safranyik,1992).

Assessment of risk classes

The results from the accuracy test from each year of the studyare presented in Fig. 5. The local Moran’s Ii demonstrated ameasureof accuracy in its description of mountain pine beetle spread be-tween 72% and 91%. Accuracy was highest in the initial years of thestudy when the mountain pine beetle infestation was relativelyminimal, which is important as it is during this period that miti-gation strategies could prove most effective at minimizing spread.Lower accuracy in later years of the study is likely a result of thelimits of adequately predicting the transition from the Constant toNull classes.

The graphical comparison between the risk and severity classesis presented in Fig. 6. The bars represent the severity classes foreach year at time t, and the sections within the bars indicate theproportion of each risk class that corresponds with the specificseverity class. One observation from the graphs is that the majorityof locations that fall within the None severity class were also in theNull risk class. In addition, the Null risk class diminishes as severityincreases. A proportion of the Light severity class was assigned tothe Null risk class suggesting that the local Moran’s Ii un-derestimates light infestations. Furthermore, there exists a smallproportion of the None class that is composed of the Increase andConstant risk classes. This indicates that the local Moran’s Ii doesnot overestimate the severity of attack when no risk is present.

The Decline risk class only constitutes a very small proportion(i.e., 0e10%) of severity classes. However, the percentages increasein later years of the infestation indicating that certain locationsexperience declining populations over time. Furthermore, thehighest percentage of the Decline class occurs in the Lightseverity class for 2005 and 2006, which likely represents thatthese locations have been under attack for multiple years, butresources are now limited forcing populations to move to otherareas.

The Increase and Constant risk classes both increase substan-tially as severity increases. Minimal proportions of these classes inthe None severity class gradually increases in the Light severityclass, and constitute the majority of the Moderate to Very Severeseverity classes. Furthermore, during the earlier years of theinfestation the Increase risk class is more prominent than theConstant class, the latter of which increases as the infestationgrows. This indicates that, in general, there are more locationsduring the earlier part of the infestation that are being colonized bylonger range dispersal (i.e., from outside a 1 km � 1 km cell) thanshort range. As the infestation grows, it is likely that populationlevels increase to the point where forest stands with low suscep-tibility now become at risk to being attacked.

Spatial distribution of risk values

The spatial distribution of risk classes for each year between2002 and 2006 are presented in Fig. 7. The maps illustrate thelocation over which beetle-induced pine mortality occurred overtime and how the spatial distribution of risk classes changes fromyear to year. The result for 2002 depicts the Constant class in west-central British Columbia as well in dispersed satellite locations, allof which confer with observations of the current epidemic (Aukemaet al., 2006). The Increase class generally surrounds the Constantclass and is also located at distances from the core of the maininfestation. Each year the Constant class grows outward from theinitial nucleus, and the Increase class remains on the frontier of theinfestation and in areas where mountain pine beetle likely engagedin longer-range dispersal. In general, most locations in the Increaseclass made the transition in later years to the Constant class asexpected.

The Decline class emerged in locations where the Constant classresided for several years. This is evident in the transition from theinitial core of the infestation shown in red in 2002 that graduallymakes the transition to the Decline class by 2006. In addition, thereare several locations across the province e mainly in the locationsdistant from the core infestation ewhere class transition occurredfrom Increase to Decline. This is evident north of the main infes-tation from 2002 to 2003, the south-eastern edge of the maininfestation between 2004 and 2005, and the scattered infestationsalong the southern border between 2005 and 2006. Many of theselocations, especially in the south-eastern edge of the main infes-tation, eventually made the transition from the Decline to Constantclass.

Discussion

In this study we aimed to investigate the utility of local in-dicators of spatial association, namely the bivariate local Moran’s Ii,as a method for estimating risk of mountain pine beetle attack oververy large areas with GIS and coarse-scale multi-temporal AOSdata. Specifically, we were interested to determine if the bivariatelocal Moran’s Ii could be used to define individual classes of riskthat could overcome the limitations of using existing methods forthe extent of the current epidemic. Rather than using a quantitativelinear rating scale as per Bone, Dragicevic, and Roberts (2005), thelocal Moran’s Ii enables a definition of risk based on changes tobeetle population levels. The qualitative risk indicators are usefulfor determining locations that are on the frontier of the infestations(i.e. the Increase class) versus locations where infestations areentrenched (i.e. the Constant class) versus those areas wherepopulations are in decline. This information is used by forestmanagers to target different areas with specific mitigation strate-gies that account for local population dynamics.

Fig. 4. Frequency of nearest neighbor distances between locations that exhibited attack in a specific year (i.e. the year represented in the title of the graph) and locations thatexhibited attack for the first time in the subsequent year. The red dotted line represents the 3 km distance selected to define the neighborhood for the bivariate local Moran’s Ii. (Forinterpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

C. Bone et al. / Applied Geography 40 (2013) 161e170166

While it is challenging to compare the accuracy of the presentedapproach with that of other risk rating systems, Zhu, Zheng, Carroll,and Aukema (2008) developed regression models with similarexplanatory power in a single year over a smaller spatial extent.However, the method presented in our study uses a strategic-leveldataset and provides a level of accuracy that would allow man-agement to prioritize mitigation activities across large areas.Furthermore, not all Moran’s Ii values were found to be significant,which means that efforts to utilize the bivariate local Moran’s Ii for

rating risk will have need to exercise caution in areas where spatialrelationships are not entirely meaningful. However, it should benoted that in this study, the number of Moran’s Ii values that werefound to be significant coincided with the area impacted bymountain pine beetle (Fig. 8). Thus, as the mountain pine beetleinfested new areas, the bivariate local Moran’s Ii captured therelationship between these locations and their surroundings.

The nature in which locations change from one risk class toanother did not always strictly adhere to the expectations

Fig. 6. The percentage of locations within each risk class (represented by percentages in

Fig. 5. Accuracy of the risk classes derived from the bivariate local Moran’s Ii in pre-dicting the change in mountain pine beetle severity.

C. Bone et al. / Applied Geography 40 (2013) 161e170 167

outlined above, but nonetheless are indicative of previous ob-servations of mountain pine beetle dynamics. For example, thereexist several locations, most notably on the frontier of the in-festations in early years, that make the transition straight fromthe Increase class to the Decline class without the populationstabilizing for any period of time. This process, previouslyobserved in some forest districts in British Columbia (Wulderet al., 2009), can be a result of either high insect mortality oran exhaustion of susceptible hosts. High mortality can be inducedfrom extreme cold temperatures during the winter months(Régnière & Bentz, 2007; Safranyik, 1989), which will cause asharp decline in populations that are on the rise. Alternatively,areas in the Decline class that had relatively high severity oneyear and a significant drop the next are likely a result of mountainpine beetle consuming available hosts and thus migrating to anew area in search of susceptible trees. Another observationregarding population dynamics is that numerous locations on thefrontier of infestations made the transition from the Increase class

side the bars) and their corresponding observed severity class as defined in Table 1.

Fig. 7. The spatial distribution of risk classes for each year of the analysis.

C. Bone et al. / Applied Geography 40 (2013) 161e170168

to the Decline or Constant class and then back to the Increaseclass, indicating that populations can become dormant in local-ized frontier locations until enough insects from the core of theinfestation reach these areas.

Fig. 8. The number of 1-hectare cells that were impacted by mountain pine beetlecontrasted the number of 1-hectare cells in which the bivariate Moran’s Ii values weredeemed significant.

The risk rating classes derived from the bivariate local Moran’s Iiare a sufficient step toward directing decision-makers on how toprioritize different areas given spread behavior. This is not to sug-gest that the Moran’s Ii is a replacement for other risk rating ap-proaches such as regression models (Robertson et al., 2008; Zhuet al., 2008). Instead there is a need to examine the integration ofqualitative and quantitative rankings at appropriate scales. Overlarge geographic arease such as the scale of the current outbreake

the bivariate local Moran’s Ii provides a means to determine wheremore precise analyses can be carried out. In areas defined by theIncrease Class, for example, regression models can be applied atfiner scales to determine where to precisely focus mitigationefforts.

Conclusion

The potential for the mountain pine beetle to move furthereastward into naïve forest environments and species (e.g., jackpine, Pinus banksiana) across the boreal forest of Canada (Safranyiket al., 2010) emphasizes the importance of developing methods tointegrate broad scale datasets in a timely manner for efficientlydevising mitigation strategies and assigning resources to areas of

C. Bone et al. / Applied Geography 40 (2013) 161e170 169

high priority. This is a common theme in insect disturbance ecologyas warming climates are leading to range expansions for a variety ofinsects, especially bark beetles in North America (Waring et al.,2009).

The GIS-based statistical method presented in this study buildson the previous research regarding risk ratings (Shore & Safranyik,1992), the use of local statistics for examiningmountain pine beetleinfestations (Long, Nelson, & Wulder, 2010; Nelson & Boots, 2008),and the use of multi-temporal spatial data for detecting changes inmountain pine beetle populations (Wulder,White, Coops, & Butson,2008). Moving forward, in order to make the local Moran’s Ii-derived risk rating system operational, broad-scale susceptibilitymeasures such as climatic variables and physiological stressesshould be incorporated to help refine areas potentially subject toattack. This could involve future climate scenarios that can estimatethe change in susceptible areas over time due to changes in tem-perature, precipitation, and other variables that have been found toinfluence beetle spread (Sambaraju et al., 2011).

Acknowledgments

This project was funded by the Government of Canada throughthe Mountain Pine Beetle Program, a three-year, $100 millionProgram administered by Natural Resources Canada, CanadianForest Service (http://mpb.cfs.nrcan.gc.ca/). Part of this researchwas undertaken by Christopher Bone as a Post Doctoral Fellow,through the NSERC Visiting Fellowships program, at the PacificForestry Centre.

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