CA Forest Management

7/29/2019 CA Forest Management

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Evaluating forest management practices using a GIS-based

cellular automata modeling approach

with multispectral imagery

Christopher Bone & Suzana Dragievi & Arthur Roberts

Received: 12 September 2005 /Accepted: 10 May 2006# Springer Science + Business Media B.V. 2006

Abstract The objective of this study was to develop an

integrated geographic information system (GIS) cellularautomata (CA) model for simulating insect-induced tree

mortality patterns in order to evaluate the influence of

different forest management activities to control insect

outbreaks. High-resolution multispectral images were used

to determine susceptibility of trees to attack, whereas the

GIS-based CA model simulated the effectiveness of clear-

cuts and thinning practices for reducing insect-induced tree

mortality. The results indicate that thinning susceptible

forests should be more effective than clear-cutting for

reducing tree loss to insect outbreaks. This study demon-

strates the benefits of an integrated approach for under-

standing and evaluating forest management activities and

expresses the need for spatial analysis and modeling for

improving forest management practices.

Keywords cellular automata (CA) . geographic information

systems (GIS) . remotesensing(RS) . spatial modeling . forest

management. forest insect outbreaks . mountain pine beetle

1 Introduction

Remote sensing (RS) and geographic information systems

(GIS) provide the opportunity to examine forest resources

and obtain insight into appropriate methods for managing

them. RS data can yield spatial information for monitor-ing forest characteristics such as species diversity [14,

38], stand density [34], and natural disturbances [25, 47,

39], among others, that are important for management

decisions. GIS can facilitate data analysis of these

characteristics through a host of spatial and statistical

approaches.

The effectiveness of RS and GIS has led to their use for

developing forest management models for determining

practical strategies. This includes combining RS and GIS

with traditional knowledge of forest practices to adapt

inventories for forest management planning [30] and for

analyzing biophysical and social patterns in order to

implement management practices [32]. However, although

such analytical models are important for management, they

are usually static representations applicable to a single

moment in time. Considering the dynamic nature of forests,

management decisions would benefit from being able to

simulate various practices in a virtual environment to

determine how management decisions affect forest structure

and processes over time. A temporal component for forest

management models can be provided by cellular automata

(CA) modeling in a GIS environment using RS data. CA

are spatially dynamic models where a set of simple

transition rules govern changes in cell states that represent

different landscape elements [1, 44]. These transition rules

explain how the current states of cells in a defined area

called the neighborhood influence the state of each cell at

some future moment in time. CA have been employed for

modeling a variety of geographic processes where land use

changes over time. Examples include modeling urban

growth [8, 9, 11, 49], land retirement [26], coastal-zone

management [23], and socioenvironmental systems [15],

among others.

Environ Model Assess

DOI 10.1007/s10666-006-9055-5

C. Bone (*) : S. Dragievi : A. Roberts

Department of Geography, Simon Fraser University,

8888 University Drive,

Burnaby, BC, Canada V5A 1S6

e-mail: [email protected]

S. Dragievi


A. Roberts



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The integration of RS, GIS, and CA is beneficial for

three main reasons. First, RS images are raster-based data

sets in which a landscape is represented by a grid of cells.

Each cell contains a value that corresponds to a specific

characteristic of the landscape. CA models traditionally use

a grid of cells to simulate dynamic processes because it

provides convenience for neighborhood calculations. Thus,

RS images can provide information in a format that isreadily used by a CA model. Furthermore, GIS provide

numerous spatial statistical tools that can be of great utility

for CA models. The use of most of these tools requires the

data to be in raster format. GIS analytical tools have been

utilized in CA models for simulating the dynamics of urban

processes [12, 43, 48] and land use change [24]. Second,

CA add a temporal component to the otherwise static nature

of RS and GIS. RS images only provide a snapshot of a

landscape at a particular moment in time, which is a

limitation for modeling phenomena that exhibit continual

change. This problem is magnified by the high costs of RS

images that make it difficult to continually obtain data atthe same rate at which a phenomenon exhibits change.

Furthermore, the tools provided in most GIS applications

are ill-equipped for representing the dynamic nature of

geographic phenomena. Therefore, CA provide a utility for

RS and GIS, as they can simulate how information captured

at a particular moment is likely to change over time. Third,

the simple CA rules governing state transition facilitate

computation efficiency [10]. High-resolution images are

large in size and contain hundreds of thousands of pixels.

As a result, the images can hinder complex applications due

to the time it takes to process information. CA, however,

typically use simple rules that evaluate local interactions

between cells, and therefore avoid the application of

complex equations applied to the entire data set; this in

turn can significantly reduce computation time.

Although these three benefits are evident in present

research, the use of CA for evaluating forest management

practices has only recently been explored. For example,

Strange et al. [42] developed a CA model to evaluate

different land use strategies to optimize afforestation (i.e.,

turning bare or harvested land into forest). Their model

used land quality and cost measures to determine the

benefits of planting different tree species as well as

transforming land to pasture. With regard to human

disturbance, a CA model, FORSAT, was developed for

simulating the dynamics of areas co-dominated by forest

and savanna that are heavily influenced by management

activities such as fires caused by humans for clearing land

[16, 17]. The results demonstrated how human influence

can dictate the location of forestsavanna boundaries.

Mathey et al. [27] provide the most evident attempt of

using CA for forest management, as they constructed a CA-

driven decision support tool for evaluating multiple

objectives for achieving sustainable forest management.

The authors considered economic, social, and environmen-

tal objectives to test the effectiveness of using CA for

simultaneously implementing different sustainability goals.

The simplicity offered through the use of CA allowed for

direct integration of expert knowledge into the simulations

of forest dynamics. These studies demonstrate that a CA

modeling approach is beneficial for understanding howanthropogenic influences affect forest processes; however,

there remains a significant gap in the literature regarding

the use of CA models for simulating natural influences such

as insect infestations and the effectiveness of management

practices for dealing with such disturbances. Furthermore,

the integration of RS, GIS, and CA for forest research in

general remains largely unexplored.

The objective of this study was to integrate a GIS-based

CA model with high-resolution RS data for evaluating

forest management decisions for dealing with insect out-

breaks. A case study of mountain pine beetle (MPB),

Dendroctonus ponderosae Hopkins, outbreaks in lodgepolepine, Pinus contorta, forests in British Columbia, Canada,

was used. Information was extracted from the thematically

classified RS data and analyzed in a GIS. The resulting data

were used in the CA model that was developed based on

the premise that MPB-induced tree mortality is largely

controlled by the susceptibility of trees to attack and the

number of MPB present in a given area [36]. The model

was first calibrated to simulate patterns of tree mortality

over a 6-year period without management intervention,

followed by implementing different strategies such as clear-

cutting and thinning to determine the effectiveness of

specific strategies at reducing the loss of timber to MPB

outbreaks.

2 MPB outbreaks and management strategies

MPB is the most serious pest of pine forests in western

North America, forcing forest managers to continually

evaluate ways to maximize yields and minimize loss of

timber revenues.

The beetle attacks both lodgepole pine and ponderosa

pine (Pinus ponderosa) in British Columbia and several

states in the western United States. It was estimated in 2005

that the current epidemic of MPB that began in the mid-

1990s had killed approximately 283 million cubic meters of

pine trees in British Columbia [19], which has serious

economic and social implications for a region that greatly

depends on timber as a source of revenue. This regional-

scale outbreak is commonly linked to: (1) decades of fire

suppression that has resulted in overmature, single-species

stands that are highly vulnerable to MPB attack, and (2) the

lack of significantly cold winters in the interior of British



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Columbia that control MPB populations. Furthermore,

preventative methods such as stand density management,

creating mixed age/species stands, and harvesting trees at

maturity are seldom employed [46], which results in

homogenous areas of susceptible pine.

In 2002, the federal government of Canada responded

to this issue by initiating the Mountain Pine Beetle

Initiative, which includes reducing the risk of attack tononinfested areas and rehabilitation to federal and private

forestlands that have be affected by the epidemic, through

both land-based and research-based programs [46]. In

2005, the provincial government of British Columbia

released the Mountain Pine Beetle Action Plan [19] with

the goal of sustaining long-term economic, social, and

environmental viability while dealing with the immediate

implications of the current epidemic. These initiatives

started to look beyond traditional direct management

techniques that are of limited use once MPB outbreaks

reach a certain level. These limited techniques include

baiting trees with a chemical attractant to draw beetlestoward a specific area, cutting infested trees and burning

them on site, applying pesticides, and harvesting dead trees

[46]. Efforts also began to focus on using various forms of

technology for understanding the complex nature of MPB

outbreaks, including the use of RS imagery for detecting

infested areas [47]. However, a problem exists with using

RS technology to manage MPB due to their life cycle

characteristics and current practices: the timing of RS

detection in relation to MPB life cycle.

MPB typically leave their currently infested trees in late

July to early August in search of a new host tree to attack.

Beetles select trees based on different characteristics, which

makes some trees far more susceptible to attack than others.

Once the new tree is selected, it is attacked by mass numbers

of beetles in order to overcome the trees defensive

mechanism, and tree mortality proceeds in the subsequent

weeks and months. The beetles lay eggs under the bark of the

tree where the offspring develop over the winter and spring

months until they are ready to emerge and search for a new

host to attack. The significant barrier for forest management

using RS to locate infested trees is that dead trees do not

exhibit signs of mortality (i.e., turn fully red) until the next

summer, at which point the insects that were born in the tree

would have left those trees in search of a new host. Early

detection is possible by late May to early June [ 31], but RS

and forestry practices have not been operationally adapted.

Therefore, current RS applications attempt to monitor

MPB typically by detecting dead but MPB-vacant trees.

This conundrum presents an opportunity to use CA for

modeling annual MPB-induced tree mortality patterns. RS

data and GIS can be utilized to provide information on

susceptibility, and a GIS-based CA model can produce

various scenarios that would allow forest management to

determine which areas are at greatest risk each year in the

future. This would also provide them with an experimental

environment to test different management strategies to

suppress new infestations and minimize the overall loss of

viable timber.

Management to reduce tree mortality and consequential-

ly to reduce MPB population levels is done through logging

and is referred to as sanitation harvesting. Harvesting canbe performed in different ways, but clear-cutting is most

commonly employed [28]. Clear-cutting involves the

removal of all trees from a given area, including both

susceptible and nonsusceptible trees. The objective is to

remove the MPB from the stand, which means harvesting

trees that show signs of attack as well as adjacent trees that

could become attacked in the near future. Therefore, clear-

cut practices attempt to remove infested and noninfested

trees in the surrounding area. The advantages of clear-

cutting is that it is the fastest way to remove a specific

volume of wood from the forest, it is the least expensive

harvesting practice, it has the greatest operational experi-ence and expertise, safety risks are better understood with

clear-cutting practices, and sites that are clear-cut provide

tolerable conditions for most commercial seedlings [40].

The disadvantages with clear-cutting as a sanitation

harvesting method are that the amount of timber that is

allowed to be cut is wasted on trees that are not susceptible,

and MPB do not typically attack trees in a uniform pattern

starting from an infestation and moving outward in

concentric stages. Furthermore, from an ecological stand-

point, clear-cuts lead to many problems such as increased

instability and soil erosion.

One way to improve the success of clear-cut methods for

managing MPB outbreaks is to define areas that are most

susceptible to MPB attack and design the shape of the

clear-cut to reflect those areas. Therefore, instead of a cut

that is symmetrically located around an infestation, the

harvest will focus more in areas that are at a greater risk of

attack. However, some low-susceptibility trees will still be

cut, as stands are not homogeneous, and some detrimental

ecological effects will persist.

An alternative to clear-cuts for sanitation harvesting is a

practice termed thinning, where only the most susceptible

trees are removed from the stand. Removing highly

susceptible pines leaves behind stronger trees and reduces

the risk of major outbreaks [7]. The decrease in density

because of thinning also reduces susceptibility by opening

the stand and altering patterns of air, light, and temperature

making it less favorable for beetles [45]. Furthermore,

thinning ensures that the stand remains intact as low-

susceptibility trees are retained, which diminishes the

ecological effects of harvesting that are apparent with

clear-cutting. Although thinning susceptible stands seems

logical, it is far more expensive to implement; therefore, the



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effectiveness of thinning for reducing tree mortality should

be evaluated in comparison to clear-cutting.

3 Methods

The methods for this study consist of three parts. First, tree

susceptibility was determined from the RS images toprovide input for the model. Second, the tree mortality

model was developed and calibrated to simulate MPB-

induced tree mortality patterns. Third, four different

management strategies were tested for reducing tree

mortality.

3.1 Defining tree susceptibility

Tree susceptibility to MPB attack was determined for a

forest area in the central interior of British Columbia. The

data for this forest area were provided by high-resolution

multispectral aerial photographs with a pixel resolution of15 cm. The RS images were collected at this resolution for

initially studying the spectral response of water loss in trees

that were attacked by MPB [31]. The high resolution of

these images also provided a utility for this study, as

individual trees can be distinguished from each other, as

seen in Fig. 1. The high costs of ground truth data and

obtaining high-resolution images limited the size of the

study area to 750 750 m; however, the area selected was

representative of forested environments in the region that

were susceptible to MPB infestations. The images were

collected during the summer of 2001, and the ground truth

data for the aerial photographs were collected in 2002 by

the British Columbia Ministry of Forestry (BC MoF), and

in 2002 by Simon Fraser University and BC MoF. The

ground truth data were used to verify classification of tree

species, tree size, and whether a tree had been attacked by

MPB. The thematically classified high-resolution imageswere analyzed in a GIS and resampled so the spatial

resolution corresponded to tree scale (i.e., each tree was one

raster cell of a digital image).

The images were analyzed to obtain information on four

variables that describe the susceptibility of a tree to MPB

attack as defined by the MPB susceptibility rating system

developed by Shore and Safranyik [41]. The four variables

were the proportion (P) of susceptible lodgepole pine in the

stand of a given tree, a location factor (L) explaining a

stands proximity to trees currently infested with MPB, a

density factor (D), and a factor of the size (S) of the tree

represented by diameter at breast height (DBH). Theoriginal rating system used the age of a tree instead of tree

size; however, trees size was selected for this study because

information on age was not available, and size can be

representative of age because diameter increases as the tree

gets older [41].

The proportion of susceptible pine (P) is an important

indicator of susceptibility because, as Hopping [21] notes,

MPB outbreaks seldom originate in mixed stands. This is

because the likelihood of MPB locating and attacking a

lodgepole pine would decrease as the number of non-

susceptible trees increases [41]. Therefore, trees located in a

stand of pure lodgepole pine (i.e., P = 1) were considered

more susceptible than those in a stand containing a high

mixture of species.

The location factor (L) explains that tree susceptibility

increases the closer a tree is to an infestation and further

increases if that infestation is relatively large. Table 1

demonstrates how the distance to and size of an infestation

influences the value of L based on the Shore and Safranyik

[41] rating system. Part (a) explains that the relative size of

an infestation in a stand (e.g., Stand 1) can be classified as

small, medium, or large depending on the number of

infested trees within 3 km of Stand 1 and the number of

trees infested within Stand 1. Part (b) uses this information

in conjunction with the distance to the nearest infestation to

provide a continuous value between 0 and 1 that represents

the variable L. The use of this rating system results in

0.06 L 1, where a value of 0.06 would indicate a stand

that is at least 4 km from a small infestation (i.e., under 900

attacked trees), whereas a value of 1 would indicate a stand

where a large number of infested trees (i.e., greater than

9000) exist within the stand. Therefore,L increases as the in-

festation draws closer and/or becomes larger. The thresholdFig. 1 High-resolution, four-band multispectral RS image of study

site located in British Columbia, Canada



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values for the Shore and Safranyik [41] rating system were

determined mainly by observations made during population

and dispersal studies [37].

The density factor (D) of trees in a stand affects

susceptibility in two ways. The first is that trees in a highly

dense stand experience greater competition for light, water,

and nutrition; therefore, trees become more stressed and

more vulnerable to MPB attack [29]. Second, stands of

lower density are believed to contain a less favorable

microclimate for MPB to successfully attack a tree and

reproduce [45]. The Shore and Safranyik [41] rating system

defines the relationship between stand density and thesusceptibility of the stand to attack by MPB. The rating

system classifies all the stands in the forest into discrete

classes, where each class receives a value describing its

susceptibility. The dotted line in Fig. 2 illustrates the

discrete susceptibility classes based on tree density. The

limitation of this component of the Shore and Safranyik

rating system is that it treats large ranges of stand densities

as having identical susceptibility. This is especially prob-

lematic in areas where stands contain a variety of densities

that fall into a single class. To overcome this limitation, a

fuzzy set approach was used to interpolate the discrete

classification rating system to produce continuous D values.

Fuzzy sets are commonly used for spatial and temporal

applications in GIS research to represent the nondiscrete

nature of geographic phenomena [13]. Classifying soil

types [6], individual trees [5], and regions of land [18] are

some examples of the variety of spatial phenomena for

which fuzzy sets have been employed; however, the use offuzzy sets with identifying susceptibility to insect infesta-

tions remains minimal [3, 4]. A fuzzy sets approach was

used here to produce a value explaining the degree (DS) to

which a stand belongs to the set of dense stands, which is

used to represent D. This was accomplished by defining a

fuzzy membership function that corresponds to the Shore

Fig. 2 Crisp classification function of

density classes versus fuzzy membership

function for the degree of belonging to

the set of(DS)

Table 1 (a) Parameters used to determine the relative size of a MPB infestation within 3 km of the stand and (b) the relative size of infestation

used in conjunction with the distance to the nearest stand to determine the value of L.

(a)

No. of infested trees outside stand within 3 km No. of infested trees inside stand

100

9000 Large Large Large

(b)

Relative infestation size Distance to nearest infestation (km)

In stand 01 12 23 34 4+

Small 0.6 0.5 0.4 0.3 0.1 0.06

Medium 0.8 0.7 0.6 0.4 0.2 0.08

Large 1.0 0.9 0.7 0.5 0.2 0.1



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and Safranyik [41] discrete function. The solid line in

Fig. 2 illustrates the fuzzy membership function. A

sigmoidal fuzzy membership function was chosen to

provide a generalized transition between values of D, and

because it is commonly employed in GIS applications using

fuzzy sets for determining continuous class boundaries

[33]. The sigmoidal function is represented by the equation

D DS 1

1 e0:0094 x472:22 ; 1

where x represents the density of trees in the stand.

The size factor (S) of a tree describes the susceptibility

of a tree based on its DBH. Larger trees are more

susceptible to MPB attack because they are typically older

with weakened defense mechanisms that cannot withstand a

mass attack of beetles [20]. The ground truth data from the

study site and information provided by [41] revealed that

trees under approximately 12 cm DBH are seldom attacked,

whereas trees over approximately 42 cm DBH receive the

highest likelihood of being attacked. This information was

used to construct a sigmoidal fuzzy membership function to

determine the degree of membership to a set of large trees,

(LT), which is used to represent S. Trees with a DBH less

than 12 cm received an S value of 0, whereas trees with a

DBH greater than 42 received an S value of 1. Trees in the

intermediate range received increasing values of S as DBH

increases. Using these parameters for defining the sigmoi-

dal function, the value of S was calculated by

S LT 1

1 e0:1599 x20:34 ; 2

where x represents DBH. The fuzzy membership function

for S is illustrated in Fig. 3.

Once the values for the variables P, L, D, and S were

calculated, they were combined so that each tree was

represented by a single value of tree susceptibility (TS). A

suitable method for calculating TS is to take the product of

the four variables. Some GIS-based studies suggest using

either the minimum or maximum value when combining

layers of continuous values; however, calculating the

product of the four variables will ensure that the influence

of each variable is included in TS. Furthermore, problems

can occur when using only the minimum or maximum value.

A tree, for example, may have a high value (i.e., close to 1)

for only one of the four variables, whereas the other threevariables are extremely close to 0. If the maximum value was

used the tree would be classified as highly susceptible,

although three of the four variables indicate that it has a very

low susceptibility to attack. Therefore, the value of TS was

calculated for each tree using the equation

TS PL D S; 3

which assumes that all variables are equally important for

determining tree susceptibility. As a result, each tree was

represented by a value between 0 and 1, representing

minimum to maximum susceptibility, respectively.

3.2 Tree mortality model

The objective of the tree mortality model was to simulate

annual MPB-induced mortality patterns of lodgepole pine

using CA and the TS values derived from the previous

section. A group of N trees was selected to be hypothet-

ically attacked by MPB at the onset of the model; this initial

stage was represented by T0. These trees acted as seeds

from which MPB would disperse to attack other trees on an

annual basis (i.e., T1, T2, ... Tn). The CA used a regional-

scale neighborhood that covered the entire study area. Thisneighborhood was selected so that all trees in the study area

had the potential of being attacked each year. The CA

transition rules explaining the process of MPB-induced tree

mortality was governed by an allometric function that

defines the number of MPB required in the neighborhood

for a tree with a given level of susceptibility to become

Fig. 3 Fuzzy membership function for the

degree of belonging to the set of(LT)



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attacked. An allometric function was chosen to follow the

logic that trees of high susceptibility required low levels of

MPB in the neighborhood to become attacked, and as MPB

populations increase to higher levels they would begin to

attack less susceptible trees [36]. Figure 4 illustrates a

potential allometric function that would be used to govern

the CA transition rules. The function explains the minimum

proportion of MPB required in the neighborhood of a tree

with a given TS value for the tree to become attacked. On

or above the curve indicates scenarios of attack, whereas

below the curve indicates scenarios of no attack. The

equation governing the allometric function is given by

y 0:05xa; 4

which explains that the proportion of beetles in the

neighborhood required for a tree of x susceptibility to

become attacked can be no less than 5% for trees of highest

susceptibility, and the proportion increases as a function of

the exponent a. The calibration of the allometric function is

described below.

At the completion of attack on lodgepole pine for a

given summer, adult MPB nest and their offspring develop

under the bark of a tree over the winter months. MPB are

highly susceptible to cold temperatures during portions of

this period [2, 22], which, during outbreaks, inflict an 80%

insect mortality rate [35]. MPB winter mortality was

simulated in this study by reducing the number of infested

trees by 80% at the end of each winter. This meant that the

trees were still dead from MPB attack, but they no longer

contained MPB that could kill more trees during the

following summer. After the simulation of winter mortality,

the susceptibility of each tree was updated to reflect the

change in the location factorL and subsequently the change

in TS. Figure 5 illustrates one complete cycle of the tree

mortality model, which is composed of the CA, MPB winter

mortality, and updating TS. Tree mortality was simulated

for six cycles to simulate MPB-induced tree mortality over a

6-year period, as this amount of time was considered

suitable for evaluating insect outbreak management.

Fig. 4 The allometric function describing the CA transition rules

Fig. 5 The tree mortality model



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The tree mortality model was calibrated to meet two

objectives. The first objective was to have the rate of tree

mortality follow a typical growth curve that is governed by

a carrying capacity. This type of growth curve explains thatthe initial exponential rate of increase in tree mortality is

eventually slowed due to a finite number of trees that exist

in the study area. The model was calibrated to coincide with

the growth curve by altering the number of time steps of the

CA that was to represent a single year. The calibration

consisted of running the CA for 1, 2, 3, 4, 5, and 6 time

steps to determine the number that resulted in annual tree

mortality that corresponds to the growth curve. The second

calibration objective was to have the most susceptible trees

attacked first, and the less susceptible trees become

attacked in future years as the MPB population in the study

area increased. This objective was set in order that themodel provides results that are congruent with the MPB

literature [36]. The exponent value of the allometric

function that defines the CA transition rules was altered to

meet this objective. Exponent values between 1.0 and

1.5 were tested to determine which one produced results

that coincided with MPB attack behavior.

3.3 Simulating forest management strategies

The objective of simulating different management strategies

was to determine how harvesting methods influence thepersistence of MPB attack. The two main strategies

compared in this study were clear-cutting and thinning.

This comparison is intended to allow management to

evaluate whether the high financial costs of thinning pro-

vide a significant reduction of trees attacked by MPB. In

addition, clear-cutting practices were evaluated based on

how the shape of the cut is defined. Square and circular

clear-cuts around the center of the infestation were first

evaluated to determine if different symmetrical cuts

influence MPB outbreaks. Next, the symmetric square and

circular clear-cuts were compared to a clear-cut that was

shaped based on susceptibility of the trees. This involvedselecting the shape of the clear-cut so that more high-

susceptibility trees were removed than low susceptibility

trees, which results in nonsymmetric clear-cut areas. This

comparison was evaluated to determine if the time and

money invested in defining a clear-cut area based on tree

susceptibility results in significantly less killed trees than

Fig. 6 (a) Classification of

study site into eight different

stands and (b) the TS

values of each tree and

initial infestation of MPB at

time T = T0

Table 2 Information extracted from RS images to calculate the variables P, L, D, and S.

Stand Percent of

lodgepole pine

Location Stand density

(trees/ha)

Range of tree

size (DBH cm)Trees infested

within stand

Trees infested

external to stand

Distance to

infestation

1 0.88 0


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the symmetric clear-cuts. These four harvesting strategies

(i.e., square clear-cut, circular clear-cut, selective clear-

cutting based on susceptibility, and thinning) were each

simulated removing seven different areas of trees.

4 Results

The study area was classified into eight different stands, as

shown in Fig. 6a, based on the density and diversity of

trees. RS data interpretation and the ground truth data were

used to obtain the information on the size distribution of

trees, the diversity and density of each stand, and the

information required to calculate the location of each stand

relative to initial infestation (Table 2). This information was

used to calculate the values of the variables P, L, D, and S

for each tree represented by a 4 4 m pixel (Table 3), which

was subsequently used to calculate the value of tree

susceptibility, TS. The TS values between 0.0 and 1.0 foreach tree are illustrated in Fig. 6b, along with the initial

simulated infestation of MPB, which acted as the seeds for

the tree mortality model.

The tree mortality model was performed for six cycles

while altering the number of time steps of the CA as well as

altering the exponent value of the allometric function until

the two calibration objectives mentioned above were met.

Regarding the first calibration objective (i.e., to have the

rate of tree mortality follow a typical growth curve that is

governed by a carrying capacity), Fig. 7 demonstrates the

tree mortality curves that were a result of using the differentnumber of CA time steps against the expected rate of tree

mortality based on a typical carrying capacity growth curve.

The figure illustrates that three time steps were most

appropriate for representing each year of tree mortality, as

the curve most closely resembles the expected curve.

The second objective (i.e., simulating an attack on the

most susceptible trees first followed by attack on less

susceptible trees in subsequent years) was satisfied by

altering the exponent of the allometric function defining the

CA transition rules. Figure 8 demonstrates how changing

the exponent value alters the height of the function. After a

heuristic evaluation of exponent values between 1.0 and1.5, it was determined that a = 1.3 was most suitable for

satisfying the second objective. Therefore, the allometric

function was governed by the equation

y 0:05x1:3: 5

Figure 9 shows the annual cumulative percentage of MPB-

induced tree mortality (thick line) that was derived using

the selected allometric function at three time steps. The

graph illustrates the MPB-induced tree mortality over time

based on equal interval classes of tree susceptibility when

using the same allometric function. The graph shows thattrees of highest susceptibility (i.e., 0.761.00) experienced

attack at a faster rate than the other susceptibility classes.

The lowest susceptibility class (0.010.25) did not experi-

Table 3 Values of the variables P, L, D, and S for each stand

calculated from the information provided in table 2.

Stand P L D S

1 0.88 0.5 0.30 0.56 0.99

2 0.98 0.5 0.70 0.56 0.99

3 0.93 0.6 0.70 0.56 0.99

4 0.78 0.8 0.87 0.56 0.99

5 0.94 0.8 0.92 0.56 0.99

6 0.00 0.5 0.13 0.56 0.99

7 0.50 0.5 0.13 0.56 0.99

8 0.50 0.5 0.13 0.56 0.99

Fig. 7 The percent of

tree mortality generated at

each cycle of the model



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ence any attack until the third time step when population

levels of MPB have increased enough to overcome the

defensive mechanisms of low-susceptibility trees. Figure 10

provides the simulated results of tree mortality at time steps

1, 3, and 6 using this equation. The two calibration

objectives can be observed through these results as follows:

(1) Tree mortality increases rapidly over the first few

iterations then declines as the number of nonattacked trees

becomes limited, and (2) areas containing high-susceptibil-

ity trees are attacked by the first time step, and trees of

lower susceptibility are attacked as each time step passes.

The calibrated model was subjected to the four different

forest management harvesting strategies. For each strategy,

seven different areas of trees were removed: 1.00, 2.25,

4.00, 6.25, 9.00, 12.25, and 16.00 ha. These seven areas of

trees were determined by increasing each side of the square

clear-cut by 50 m. Each strategy is illustrated in Fig. 11

for the minimum (1 ha) and maximum (16 ha) area of trees

removed. The square and circle clear-cuts were locatedbased on having the infestation as the center of the clear-

cut. The location of the selective clear-cut was focused on

the susceptibility of trees. Therefore, instead of a symmetric

clear-cut, the shape of the cut followed the contours of the

stands that contained the trees of highest susceptibility.

Harvesting was thus focused in stands 4 and 5, whereas

minimal trees were removed from stand 3 (see Fig. 6).

The thinning management strategy involved harvesting a

quantity of the most susceptible trees that was equivalent in

area to the clear-cut strategies. Therefore, an equivalent of

1 ha of the most susceptible trees were removed for the

1-ha harvesting scenario, whereas an equivalent of 16 ha ofthe most susceptible trees were removed for the 16-ha

harvesting scenario. The tree mortality model was per-

formed using each management strategy for a total of six

time steps. Figure 12 shows how tree mortality was affected

by implementing each scenario. The graph shows the

percent of trees remaining after harvesting that were

attacked and killed by MPB.

The results from the tree mortality model simulations

displayed in Fig. 12 conclude that the choice of harvesting

practice has significant consequences on the number of

trees that are attacked by MPB. The most pertinent

Fig. 8 The influence of the exponent value on the allometric function

Fig. 9 MPB-induced tree mor-

tality over time using the

calibrated allometric function



11/15

observation was the success of the thinning harvesting

strategy over the clear-cut practices for reducing tree

mortality. Whereas thinning of 1 ha and 2.25 ha areas

showed no significant difference, thinning of 4 ha and

beyond displayed a dramatic decrease in tree mortality. The

reason for this was that the most susceptible trees in the

study area were removed, which severely debilitated the rate

at which the MPB population could increase. Furthermore,

thinning also decreases the tree density of a stand, which in

turn decreases the overall susceptibility to MPB attack.

Thinning works better at reducing tree mortality than do

clear-cuts because the latter strategy focuses all harvesting

efforts in a centralized area around the infestation, whereas

thinning will remove the same number of trees over a

greater area, thus having a regional-scale effect. Therefore,

as the results presented in Fig. 12 illustrate, less harvest-

ing is required with thinning to minimize timber loss to

MPB attack. With regard to forest management, these

results suggest that the high costs of thinning are warranted

if reducing tree mortality from MPB is a priority. However,

thinning efforts must take into consideration the minimal

number of trees that should be removed to prevent tree

mortality. Figure 12 demonstrates that although thinning is

most effective, it may not be useful if performed on a small

volume of wood. Therefore, a challenge for future research

is to determine the minimal effective thinning volume

required for different levels of initial MPB attack.

Examining the results from the three clear-cut methods

illustrates that the shape of the clear-cut does not have an

impact on tree mortality if the cut is symmetrically placed

around the infestation. Both the square and circle clear-cut

approaches exhibited minimal success with reducing timber

loss to MPB even when increasing the size of the harvest.

This was evident in that the loss of timber was only reduced

by 30% for both methods when comparing a 1-ha harvest to

a 16-ha harvest. Conversely, the other two methods reduced

tree mortality by approximately 80% when comparing a

1-ha to 16-ha harvest. The lack of success for the square

and circle clear-cuts was because trees were removed

regardless of their susceptibility to attack. Low-susceptibil-

ity trees were removed even though they were at minimal

risk of attack during the initial MPB population level,

which meant that less high susceptibility trees could be

harvested. Since MPB have the ability to disperse distances

Fig. 10 Results from the model

simulation of MPB-induced

tree mortality patterns for T1,

T3, and T6

Fig. 11 Harvesting strategies simulated in the study area at time

T = T0 for 1-ha harvest (left) and 16-ha harvest (right)



12/15

throughout the study area, the square and circle clear-cuts

did not prevent them from attacking high-susceptible trees.

Therefore, for this technology to be at all successful,

management would have to develop large-scale clear-cutting

plans to produce a significant decline in tree mortality.

However, as clear-cuts become larger their detrimental effects

to the ecology of the forest become magnified, which in turn

could prevent the forest from being a viable source of timber.

The selective clear-cut displayed intermediate results, as

tree mortality was reduced when using the 9-ha harvest. This

was an improvement over the other two clear-cut methods

because the shape of the cut was selected based on where the

most susceptible trees were located rather than being based

on the distance to the center of the infestation. However, the

method proved not as successful as thinning because clear-

cutting ensures that some low-susceptible trees will still be

removed. Selective clear-cutting could provide an interme-

diate strategy that balances the affordability of simple clear-

cutting and the effectiveness of thinning. Some forest

managers may not have the financial resources or the time

to implement thinning harvesting, but would be able to

benefit from clear-cutting areas based on susceptibility.

Although selective clear-cutting is not as effective as

thinning, Fig. 12 indicates that when selective cutting is

applied over large enough areas it can have similar results.

5 Conclusion

The results from this study indicate that the size or the

shape of the harvest is not the most important factor when

attempting to reduce tree loss to MPB attacks; instead, the

susceptibility of trees should be the focus of management

activities. As tree susceptibility can vary at the local scale,

practices such as clear-cuts that invoke a spatially homo-

geneous response to insect outbreaks are not as appropriate

because they ignore local-scale variability. Thinning prac-

tices that acknowledge individual tree susceptibility are

more useful, as the most susceptible trees can be identified

and removed while retaining important ecological compo-

nents of the forest. Thus, the high-resolution RS data were

an essential component of this study as they enabled

susceptibility to be defined at the tree level.

The disadvantage of using high-resolution images is that

they are costly, which can restrict the scale over which data

are collected. This presents a conundrum for studies such as

this where high-resolution is necessary for distinguishing

individual trees, but the scale of the study site limits the

quantity of information that is available for determining tree

susceptibility. For example, the location factor L deter-

mined the susceptibility of a stand using the number of

trees attacked at a given distance to the stand. The Shore

and Safranyik [41] rating system explains that a stand is

susceptible if trees are attacked within a distance of 3 km,

but the study site covered only a portion of this distance.

This can lead to underestimating the susceptibility of a

stand to MPB attack because detecting infested trees within

3 km is limited by the size of the study area. For this study,

the initial infestation occurred within the study area, which

resulted in a relatively high susceptibility rating for some

stands regardless of whether there were infestations outside

the study area. However, the susceptibility rating for all

stands could still be higher if a significant number of trees

were infested beyond the boundaries of the study area but

Fig. 12 Tree mortality at time

T = T6 for each harvesting

practice for different

harvesting sizes



13/15

within 3 km. Although this issue presents a limitation for

this study, it does not discredit the findings, as the annual

increase in attack followed a logical exponential curve that

is representative of MPB-induced tree mortality. Tree

mortality increases exponentially until availability of

susceptible trees becomes exhausted. Therefore, although

tree susceptibility may have been slightly underestimated,

the rate of attack was still a close representation of realityand allowed for effective evaluation of the objective of this

study, which was to analyze the influence of different

management strategies for controlling MPB outbreaks. This

demonstrates that although larger study sites are optimal for

providing adequate information, the model can be applied

across a range of spatial scales for determining the

implications of MPB attack and management activities.

Thus, even when only large-scale images are available,

simulating the dynamics of infestations should precede

harvesting decisions.

The use of GIS was beneficial to this study as it provided

methods in this study for calculating the susceptibility oftrees by measuring the susceptibility variables and effec-

tively combining them to produce an output demonstrating

the variability of susceptibility across the forest landscape.

GIS are a utility for forest management because the spatial

relationships between individual trees and stands can be

evaluated and integrated into management decisions.

However, GIS and RS data have limited predictive

capabilities, as they usually provide static representations

of the world. This study provided an opportunity to

integrate the RS data and GIS with CA for simulating

patterns of tree mortality and evaluating appropriate

management decisions.

The CA model proved useful for simulating insect

propagation and evaluating management practices. The

parameters were specified so that the model can be applied

to a variety of scales and locations that are susceptible to

MPB infestations. The model could be incorporated as a

decision-support tool where interested stakeholders can use

GIS as a virtual laboratory to change parameters, such as the

initial size and location of the infestation, growth and

mortality rates, and dispersal distances, to determine how

life-cycle characteristics of MPB affect tree mortality. The

model also provides the potential for creating different

scenarios to evaluate appropriate practices for managing

forests in anticipation of insect outbreaks. For example,

species diversity or stand density can be altered in the GIS,

and resulting data could be run in the CA to determine how

important these variables are compared to one another for

influencing MPB attack. CA are advantageous in this respect

because numerous stakeholders with a variety of back-

grounds can collaborate to determine a desirable outcome.

Unlike typical models based on partial differential equations

that are mathematically intensive, explicit knowledge of the

system is not required for creating a valid CA model because

the necessary information for the modeled process is

included in the form of rules rather than mathematical

equations. This allows for direct incorporation of knowledge

from experts that is not necessarily restricted to hard data,

and is particularly useful when attempting to model prob-

lems that are complex. Furthermore, the outputs from the

model simulations provide management with a visualunderstanding of how MPB are most likely to disperse

through the forest and the related effectiveness of different

practices they may wish to implement.

Collectively, RS, GIS and spatial modeling with CA

provide forest and other natural resource managers with the

opportunity to investigate natural processes in both space

and time and facilitate the evaluation of management

practices to determine effective measures for dealing with

ecological problems such as insect infestations.

Acknowledgments The authors are thankful to the Natural Sciences

and Engineering Research Council (NSERC) of Canada for full

support of this study under the Discovery Grant awarded to the second

author. Acquisitions of high-resolution data sets used in this study are

funded from BC Forestry Innovation and Forestry Investment Account

grants awarded to the third author.

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