1. Decision Analysis to Evaluate Control
Strategies for Crested Wheatgrass
(Agropyron cristatum) in Grasslands
National Park of Canada
Leonardo Frid and John F. Wilmshurst*
Protected area managers often face uncertainty when managing invasive plants at the landscape scale. Crested
wheatgrass, a popular forage crop in the Great Plains since the 1930s, is an aggressive invader of native grassland and
a problem for land managers in protected areas where seeded roadsides and abandoned fields encroach into the
native mixed-grass prairie. Given limited resources, land managers need to determine the best strategy for reducing
the cover of crested wheatgrass. However, there is a high degree of uncertainty associated with the dynamics of
crested wheatgrass spread and control. To compare alternative management strategies for crested wheatgrass in the
face of uncertainty, we conducted a decision analysis based on information from Grasslands National Park. Our
analysis involves the use of a spatially explicit model that incorporates alternative management strategies and
hypotheses about crested wheatgrass spread and control dynamics. Using a decision tree and assigning probabilities
to our alternative hypotheses, we calculated the expected outcome of each management alternative and ranked these
alternatives. Because the probabilities assigned to alternative hypotheses are also uncertain, we conducted a sensitivity
analysis of the full probability space. Our results show that under current funding levels it is always best to prioritize
the early detection and control of new infestations. Monitoring the effectiveness of control is paramount to long-
term success, emphasising the need for adaptive approaches to invasive plant management. This type of decision
analysis approach could be applied to other invasive plants where there is a need to find management strategies that
are robust to uncertainty in the current understanding of how these plants are best managed.
Nomenclature: Crested wheatgrass, Agropyron cristatum (L.) Gaertn.
Key words: Decision analysis, simulation modeling, alien plant invasions.
Alien plant invasions threaten biodiversity, ecosystem
services and human activities globally (Mooney 2005).
Significant resources are expended around the world on the
prevention of new invasions and on the control of existing
ones (Perrings et al. 2005). While at a small scale control
efforts can be highly effective, for the most part, managers
attempting to control invasive plants at landscape scales are
fighting losing battles (Rejmanek et al. 2005). Failure of
control efforts at large spatial scales is, in part, driven by
our lack of species and landscape specific information
about the distribution and spread of the invaders (Shea and
Chesson 2002). Unfortunately, this type of information is
difficult to obtain and requires precious time that is then
lost for control efforts. Land managers require tools that
allow them to choose the most suitable management
strategy to control invasive species in the face of
uncertainty. One such tool, decision analysis, can be used
to rank alternative management decisions (Clemen 1996;
Peterman and Anderson 1999). Decision analysis is
commonly used in fields such as fisheries management
(Alexander et al. 2006; Peters and Marmorek 2001; Peters
et al. 2006) but there are few examples of its use in invasive
species management (Maguire 2004). Here we present
decision analysis as a tool in invasive species management
planning through the example of crested wheatgrass
[Agropyron cristatum (L.) Gaertn.] in Grasslands National
Park.
DOI: 10.1614/IPSM-09-006.1
* First author: Senior Systems Ecologist, ESSA Technologies Ltd.,
1765 West 8th Avenue, Suite 300, Vancouver, BC, Canada V6J
5C6; second author: Ecologist, Parks Canada, Western and
Northern Service Centre, 145 McDermot Ave., Winnipeg, MB,
Canada, R3B 0R9. Current address of second author: Jasper
National Park of Canada, P.O. Box 10, Jasper, AB, Canada T0E
1E0. Corresponding author’s E-mail: lfrid@essa.com
Invasive Plant Science and Management 2009 2:324–336
324 N Invasive Plant Science and Management 2, October–December 2009

2. Crested wheatgrass was introduced into the North
American Great Plains from Eurasia in the 1800s
and gained importance as a forage crop for grazing and
hay in the 1930s (Dillman 1946; Henderson 2005; Rogler
and Lorenz 1983). While the popularity of crested
wheatgrass as a crop continues, its propensity to invade
undisturbed rangeland (Hull and Klomp 1967; Marlette
and Anderson 1986), particularly east of the continental
divide (Henderson 2005), makes it an undesirable
species in communities where the preservation of native
grassland is a management objective. This is the case in
Grasslands National Park, Saskatchewan, Canada, where
crested wheatgrass spreads from hay fields, pipelines, and
road rights-of-ways into surrounding native mixed-grass
prairie.
Natural area managers and researchers have worked for
years to determine the best methods to stop crested
wheatgrass encroachment (Bakker et al. 1997; Bakker and
Wilson 2001; Christian and Wilson 1999; Hansen 2007;
Hansen and Wilson 2006; Henderson 2005) and restore
invaded areas (Ambrose and Wilson 2003; Bakker and
Wilson 2004; Parks Canada Agency 2002; Sturch 2005;
Wilson et al. 2004). These efforts have provided valuable
information on the invasion biology of crested wheatgrass
and have resulted in methods of control and restoration
that have proven effective at site specific scales in the short
(Sturch 2005) and long (Bakker and Wilson 2004) term.
However, understanding how to eradicate crested wheat-
grass in small patches, and restore these patches to native
vegetation, is only the first step in managing this ecosystem.
A strategy is needed to control crested wheatgrass spread
and decrease its cover at landscape scales over long time
periods.
Given limited financial resources, crested wheatgrass
control will take years, and likely decades, so a strategy that
maximizes the long-term effectiveness is required. Our
objective is to determine how land managers can best
allocate limited funds for crested wheatgrass control and
restoration, to provide the greatest and fastest reduction in
crested wheatgrass cover over the next 50 yr.
One of the first decisions that must be made when
allocating limited resources to the control of invasive plants
is whether to focus on known existing large infestations or
on finding and controlling inconspicuous small nascent
foci. Moody and Mack (1988) showed that under certain
conditions it is more effective to prioritize small nascent
foci for management, but Wadsworth et al. (2000) found
that this may not be the case for plants that spread mainly
by long-distance dispersal. These two findings highlight the
need for a detailed understanding of the natural history of
invasive species to enable managers to make decisions on
treatment priorities.
Managers must also decide how many resources to
devote to invasive management. Various studies have
shown that spending less in the short term can be
more costly in the long term (Higgins et al. 2000a;
Pimentel et al. 2000). However, allocating more resources
to controlling invasive plants is almost always at the
expense of other management priorities, underscoring the
need for an ecological cost-benefit analysis to justify
significant expenditures (Andersen et al. 2004). It is
therefore important to evaluate the relative long-term
benefits of making these short-term sacrifices (Taylor and
Hastings 2004).
To protect the remaining tracts of native mixed-grass
prairie, ecologists from Grasslands National Park are
currently considering a variety of alternative actions in
their crested wheatgrass control program. Three decisions,
common in invasive species management, need to be made.
First, should an investment be made in extraordinary short-
term control efforts to achieve greater benefits in the long
term; second, should control and restoration focus on
emergent or established infestations; and finally, how
should the effort be partitioned between monitoring,
control, and restoration? These decisions must be made
in the face of uncertainty in three key components of the
system: (1) the effectiveness of restoration and control
efforts, (2) the rate of spread of existing patches, and (3) the
rate of increase in newly infested, initially small patches. To
aid decision making and to identify knowledge gaps in our
understanding of the invasive biology of crested wheatgrass
(Byers et al. 2002) we developed simulation models to
reflect both management actions and alternative hypotheses
about the dynamics of crested wheatgrass spread and
control. We then applied the technique of decision analysis
(Clemen 1996; Ellison 1996; Peterman and Anderson
1999; Peterman and Peters 1998) to analyze our model
results and rank management alternatives for crested
wheatgrass given uncertainty.
Interpretive Summary
The decision analysis approach integrates biological, economic,
logistical, and, if relevant, sociological information and constraints
to meeting any management challenge. The challenge is to gather
relevant data on these disparate elements to apply to the model.
Much of this can be gathered using the principles of adaptive
management. By keeping track of successes, failures, and the costs
of implementing alternative control strategies, sufficient
information will be available for a formal decision analysis
process. However, the key is to consider alternatives. The
information we present through this example is appropriate to
any invasive plant management problem that involves decisions
about resource allocation and alternative strategies, as well as
uncertainty about the underlying dynamics of the natural and
management systems. We suggest that rather than adopting an ad-
hoc approach to invasive plant management by following the
status quo or applying rules of thumb, managers should explicitly
consider uncertainty and challenge alternative management
strategies by following a decision analysis approach.
Frid and Wilmshurst: Crested wheatgrass decision analysis N 325

3. Materials and Methods
Study Area. Grasslands National Park (42,368 ha,
49u159N, 107u09W) was established in 1988 to preserve
a representative portion of the Canadian mixed-grass
prairie ecosystem (Figure 1). The climate is considered
subhumid; winters are long, cold, and dry, while summers
are short and hot. Mean daily temperature ranges from
15 C below zero in January to 20 C (68 uF) in July. Total
annual precipitation averages 325 mm (12.8 in), with most
falling as rain in the spring months, and approximately
one-third falling as snow in the winter. The growing season
in the park is relatively short, averaging 170 d between
killing frosts, but low moisture availability often reduces its
length further (Loveridge and Potyondi 1983).
We subdivided the park into five biophysical units based
upon the vegetation inventory of the park (Michalsky and
Ellis 1994): upland grassland, sloped grassland, valley
grassland, shrub communities, and eroded communities.
Crested wheatgrass can be found in all of these biophysical
units. While it has been seeded as a hay crop in the upland
and valley grasslands, and in some cases the shrub
community (the riparian zone in the park), it has spread
into the sloped grasslands and eroded communities.
Decision Analysis Framework. We calculated the conse-
quences of alternative management strategies to control
crested wheatgrass, probability weighted by our alternative
hypotheses for the rate of spread, the effectiveness of
control, and the rate at which new patches appear on the
landscape. Our decision analysis had six components: (1)
alternative actions, (2) performance measures, (3) uncer-
tainties related to the dynamics of crested wheatgrass spread
and control, (4) a model to predict outcomes, (5) a
decision tree, and (6) sensitivity analyses. Each of these
components is described below.
Alternative Actions. We considered alternative strategies
based on four possible combinations of two management
components: the annual budget allocated to crested
wheatgrass treatment (high or low) and the prioritization
strategy of treating large existing patches vs. small new
populations. Two alternative budgets were expressed as a
ceiling on the annual area that could be treated. The
revegetation action plan for the park sets a goal of 45 to
65 ha/yr (111 to 161 ac) of restoration in the park (Sturch
2000). The budget alternatives represent the revegetation
action plan (50 ha/yr), and a doubling of the area allocated
for restoration (100 ha/yr) simulated at a resolution of
Figure 1. Location of Grasslands National Park. Solid lines show the current park land holdings. Areas in white represent old fields
(mapped in 1994) seeded with crested wheatgrass.
326 N Invasive Plant Science and Management 2, October–December 2009

4. 1 ha. For large patches, the cost of restoration is about
$1,200 Canadian (Cdn)/ha, which includes the cost of
chemical treatment ($60), native seed ($1,100), equipment
and labor ($40). Therefore, our budget alternatives
represent annual expenditures of approximately $60,000
and $120,000 Cdn annually for the low and high budget
scenarios, respectively. The cost of treating the small
patches is considered to be much lower (approximately
$100/ha) because heavy equipment and native seed is not
required. At this rate, treating 50 ha of small new patches
only would leave $55,000 to allocate to monitoring costs.
About 2 ha can be monitored by a worker per day. At $20/
hr, this budget would allow for close to 690 ha of
monitoring for small new patches per year under the low
budget scenario. Thus, our alternative strategies consider
the trade-off between applying all available resources to
containing large known infestations vs. investing some
resources in early detection in order to control small new
infestations before they become established. As a bench-
mark we also considered inaction (no treatment) as a
hypothetical alternative.
Performance Measures. The performance measures we
used to evaluate each combination were (1) the cumulative
area treated over a 50 yr period as an indicator of the total
cost of each treatment strategy, and (2) the cumulative area
covered by crested wheatgrass over that period, as an
indicator of the outcome of each management strategy. We
chose the cumulative area invaded by crested wheatgrass,
the sum of the area of the park covered by crested
wheatgrass each year across all years, rather than simply the
final area at year fifty to track both the rate and magnitude
of change in crested wheatgrass cover over time. Model
results are reported as area treated and cumulative area
covered by crested wheatgrass over the simulation time
period.
Uncertainties. We focused our analysis of uncertainty on
what are perceived to be three key unknowns in crested
wheatgrass dynamics. These are (1) the rate at which
patches spread across the landscape over time, (2) the rate
at which new patches appear via long-distance dispersal,
and (3) the effectiveness of site-specific control efforts.
The invasion of crested wheatgrass follows two distinct
patterns. The first is the expansion of hay field margins.
Fields of crested wheatgrass generally spread into the native
prairie along their windward margin via seed dispersal
(Hansen 2006). Crested wheatgrass produces prodigious
amounts of seed (Cook et al. 1958; Pyke 1990) and the
seed establishes readily, accounting for its popularity as a
hay crop (Rogler 1954). This seed is wind dispersed short
distances by rolling over hard ground or snow, resulting in
a field that can creep upwards of 1 m/yr from a seeded field
margin (Ambrose and Wilson 2003; Henderson 2005).
The shape of the dispersal kernel of crested wheatgrass is
known from only a few unpublished studies (Darcy
Henderson, personal communication). Recent work in
the Canadian prairie has successfully used a hyperbolic
Pareto distribution to model seed dispersal for invasive wild
oats (Avena fatua L.) (Shirtliffe et al. 2002). We also used
the Pareto distribution to model the dispersal kernel for
crested wheatgrass (Equation 1).
P Spreadvxð Þ~1{
xm
x
a
½1Š
where xm, the minimum spread distance, is set at 0.5 m
(Henderson 2005) and a is the shape parameter. Because
what is most important about a dispersal kernel is not its
mean distance but the shape of its tail (Clark and Fastie
1998), we modeled fast spread using a fat-tailed dispersal
kernel (a 5 2.01) and a slow spread using a narrow-tailed
dispersal kernel (a 5 3). The mean annual spread distance
between the slow-spread rate (0.75 m/yr) and the fast-
spread rate (0.995 m/yr) differs only by a factor of 1.32,
but the 99th percentile, 2.4 m vs. 5 m, differs by a factor of
2.08. The mean spread rates are within the range of what
has been observed (Henderson 2005), but there is
uncertainty around the shape of the distribution.
The second form of spread is the long-distance dispersal
of crested wheatgrass seed, likely in herbivore dung. This
form manifests itself as satellite plants or small patches
appearing far distances from the nearest seed source. These
plants, which can be found in every vegetation community
in the park, become a seed source for short-distance
dispersal. As a result, unexpected patches of crested
wheatgrass can appear in otherwise undisturbed areas of
the park, and left unmanaged, these can grow to become
large invaded areas. While these are routinely observed in
the park, we only have limited information about the rate
at which these new patches of crested wheatgrass appear.
Therefore we set two rates: many (average of two new
satellites per year) and few (average of one new satellite per
year) (Table 1, electronic appendix). The actual number of
new infestations in the park was modeled using the Poisson
distribution with mean values of 1 and 2 to differentiate
between many and few satellites.
The effectiveness of control efforts is another factor that
is considered highly uncertain. While recent restoration
research has provided the park with effective tools for
eliminating crested wheatgrass (Bakker and Wilson 2004;
Hansen and Wilson 2006; Sturch 2005; Wilson and Gerry
1995; Wilson and Pa¨rtel 2003), there is still variability in
the effectiveness and persistent benefit of these techniques.
Based upon experience in the park, control effectiveness
can vary between complete elimination of crested wheat-
grass, to setting the crested wheatgrass back such that it
persists but does not spread (effective), to failure, in which
spread continuous unabated (ineffective). Hence, we varied
the probabilities of these outcomes for two levels of relative
Frid and Wilmshurst: Crested wheatgrass decision analysis N 327

5. control effectiveness (effective and ineffective) for new
crested wheatgrass infestations.
Model. We developed a spatially explicit simulation model
to compare the different landscape level control strategies
and to determine the sensitivity of each strategy to
uncertainty in the spread dynamics of crested wheatgrass.
The model consists of two main components: first, a state
and transition vegetation model that considers the site-
specific dynamics of crested wheatgrass succession and
control at a 1 ha scale, and second, a spatially explicit
spread model that considers how crested wheatgrass arrives
at uninvaded areas from within invaded areas or from
outside of the modeled landscape.
We developed our state and transition models using The
Vegetation Dynamics Development Tool (VDDT).1
Table 1. Simulation results for all 36 possible combinations of strategy and hypotheses for control effectiveness, spread rates, and
satellite events. Results are shown in terms of cumulative coverage by crested wheatgrass and cumulative treatments over a 50-yr period.
Fast and slow spread are modeled using the Pareto shape parameters of 2.01 (fast) and 3 (slow), and as 10 and 15 yr, respectively, for a
polygon to transition into the established state after invasion. Few and many satellites are modelled as Poisson mean values of 1 and 2
respectively to determine the number of new patches appearing from outside the landscape.
Strategy and budget
Hypotheses Cumulative area results (ha [ac])
Control Spread Satellites Invaded Treated
No management NA Fast Many 53,568 [132,169] 0 [0]
Few 52,743 [130,330] 0 [0]
Slow Many 45,769 [113,097] 0 [0]
Few 45,611 [112,707] 0 [0]
Large patches—100 ha Effective Fast Many 6,240 [15419] 1,179 [2,913]
Few 6,189 [15,293] 1,162 [2,871]
Slow Many 6,263 [15,476] 1,103 [2,725]
Few 6,141 [15,175] 1,067 [2,636]
Ineffective Fast Many 17,629 [43,562] 2,675 [6,610]
Few 17,143 [42,361] 2,684 [6,632]
Slow Many 12,505 [30,900] 2,157 [5,330]
Few 12,622 [31,189] 2,161 [5,339]
Large patches—50 ha Effective Fast Many 18,446 [45,581] 1,463 [3,615]
Few 18,792 [46,436] 1,464 [3,617]
Slow Many 13,359 [33,011] 1,372 [3,390]
Few 12,872 [31,807] 1,330 [3,286]
Ineffective Fast Many 33,971 [83,944] 1,702 [4,205]
Few 35,188 [86,951] 1,796 [4,437]
Slow Many 27,028 [66,787] 1,637 [4,045]
Few 27,167 [67,131] 1,629 [4,025]
Small patches—100 ha Effective Fast Many 6,813 [16,835] 1,129 [2,789]
Few 6,948 [17,169] 1,106 [2,732]
Slow Many 6,630 [16,383] 1,082 [2,673]
Few 6,726 [16,620] 1,070 [2,644]
Ineffective Fast Many 13,850 [34,223] 2,068 [5,110]
Few 13,292 [32,845] 2,018 [4,986]
Slow Many 12,924 [31,935] 1,931 [4,771]
Few 11,938 [29,499] 1,821 [4,499]
Small patches—50 ha Effective Fast Many 15,387 [38,021] 1,272 [3,143]
Few 14,651 [36,203] 1,241 [3,066]
Slow Many 13,325 [32,926] 1,123 [2,774]
Few 12,585 [31,098] 1,101 [2,720]
Ineffective Fast Many 31,014 [76,636] 1,414 [3,494]
Few 30,178 [74,571] 1,450 [3,583]
Slow Many 25,823 [63,809] 1,419 [3,506]
Few 25,770 [63,678] 1,437 [3,550]
328 N Invasive Plant Science and Management 2, October–December 2009

6. VDDT is a software tool for creating and simulating semi
Markovian state and transition models (ESSA Technologies
Ltd. 2005b). VDDT has been used to simulate various
ecosystems including the dynamics and restoration of
sagebrush steppe communities (Forbis et al. 2006), historic
fire regimes across the continental United States for the
LANDFIRE project (Anonymous 2009) and others
(Arbaugh et al. 2000; Hemstrom et al. 2001; Merzenich
and Frid 2005; Merzenich et al. 1999).
Models developed in VDDT outline the possible
vegetation states of the landscape as well as transitions
between states. These transitions are either deterministic
and occur after a fixed period of time, or stochastic, having
a given probability of occurring each annual time-step.
VDDT models are simulated numerically and track both
the state of the landscape over time as well as the
occurrence of transitions.
The model we developed for crested wheatgrass consists
of three possible states: uninvaded, invaded, and established
(Figure 2). The uninvaded state represents a polygon in
which crested wheatgrass is absent. From this uninvaded
state, a polygon can transition to the invaded state through
invasion either by spread from a neighboring polygon that
is invaded, or by long-distance dispersal. The invaded state
represents a polygon that has detectable levels of crested
wheatgrass, but in which other plant species are still
dominant. Polygons in the invaded state act as weak
sources of crested wheatgrass to neighboring polygons.
Management efforts applied to crested wheatgrass in
invaded polygons frequently result in control, returning
the polygon to the uninvaded state. Occasionally, manage-
ment efforts may reduce the cover of crested wheatgrass in a
polygon without accomplishing a transition back to the
uninvaded state. It is also possible that if management is
applied incorrectly or under the wrong environmental
conditions, there will be no effect on the state of the
polygon. If enough time elapses in the invaded state
without effective management, a polygon will transition
into the established state. Under the fast-spread hypothesis
we set the time to transition to the established state at
10 yr, vs. 15 yr for the slow-spread hypothesis. These
values were set based on personal communications with
managers at the park.
The established state represents a polygon in which
crested wheatgrass is the dominant vegetation type.
Polygons in this state act as strong sources of crested
wheatgrass to neighboring polygons. Management efforts
applied to crested wheatgrass in the established state rarely
result in control back to the uninvaded state, but may
frequently result in the reduction of enough cover to
transition a polygon from the established to the invaded
state. However, the failure of management efforts to have
any impact in the established state is also relatively
frequent.
By itself, the state and transition model shown in Figure 2
is not spatially explicit and describes only the dynamics of
crested wheatgrass within each 1 ha polygon. We simulated
the spread of weeds among polygons in our five biophysical
units using the Tool for Exploratory Landscape Scenario
Analyses (TELSA).2
TELSA was developed to simulate
landscape-level terrestrial ecosystem dynamics over time, to
assist land managers in assessing the consequences of various
management strategies (Beukema et al. 2003; ESSA
Technologies Ltd. 2005a; Kurz et al. 2000).
For this study, the inputs for our TELSA simulations in
each landscape include
1. state and transition models (Figure 2) for the five
vegetation communities in the landscape
2. spatial, geographic information system (GIS) data layers
representing vegetation communities and the current
crested wheatgrass distribution of the landscape
3. parameters governing the spatial spread and control of
crested wheatgrass (These parameters include the
probability distribution of neighbor-to-neighbor spread
distance at each annual time-step and the average
number [Poisson] of new infestations from outside the
landscape at each time-step.)
Input polygons defining the initial state and vegetation
community of the landscape are subdivided into simulation
polygons through a process called ‘‘Voronoi Tessellation’’
(Kurz et al. 2000). Unlike the use of a grid, this process
divides original polygons into smaller units for simulation
without losing any of the original boundary information.
While computationally more demanding, the resolution of
features that are important for weed spread, such as riparian
and transportation corridors, is maintained. We used
49,602 simulation polygons with an average size of 0.85 6
0.001 ha (mean 6 standard error [SE]).
The creation of new infestations depends upon the
relative probability that any polygon in the park could be
invaded by crested wheatgrass via long-distance dispersal,
Figure 2. State and transition model for crested wheatgrass
dynamics. Invasion is a stochastic process influenced by
proximity to neighboring infestations and vegetation communi-
ty. Escape to an established infestation occurs after 10 to 15 yr of
inaction. Control efforts can set back population densities of
crested wheatgrass, eradicate the population, or fail to have
any effect.
Frid and Wilmshurst: Crested wheatgrass decision analysis N 329

7. which is a function of the vegetation community within
which it resides. Based on random sampling in the park,
Hansen (2006) reported the area of crested wheatgrass
invasion in vegetation communities in Grasslands National
Park. We converted these to proportional vulnerabilities,
and using these proportions, ranked invasion susceptibility
(from most to least invaded) as valley grassland, shrub
community, sloped grassland, upland grassland, and
eroded community. Given that most of our crested
wheatgrass source communities are in valley grasslands,
our probabilities are calculated relative to the valley
grassland landscape position. Based on these rankings, the
relative susceptibility of each of these communities to
crested wheatgrass invasion is valley grassland 1, sloped
grassland 0.68, shrub community 0.68, upland grassland
0.59, and eroded community 0.18 (Hansen 2006). These,
then, are the relative probabilities that each of these
communities in the simulations would be invaded by long-
distance dispersal; probabilities that also serve to scale the
relative rates that these communities are invaded by short-
distance dispersal. For example, if there were equal areas of
valley grassland and upland grassland in the landscape, a new
long-distance dispersal event would only be 59% as likely to
occur in the upland grassland as in the valley grassland. For
short-distance dispersal, spread into the upland grassland
would be on average only 59% as far as into the valley
grassland. For simulating long-distance dispersal, we used
the Poisson distribution to describe the number of new
patches of crested wheatgrass appearing in the park annually.
As alternatives, we modeled long-distance dispersal as mean
numbers of new patches being equal to one or two per year.
These we identify in the text as few or many patches
respectively. Given that there is no information available on
long-distance patch establishment for crested wheatgrass, we
chose these values as they spanned a reasonable range of
patch densities in model simulations. We will discuss the
implications of altering these values.
After the simulation of new infestations, the model
simulates the expansion of existing infestations between
adjacent polygons. For each polygon already occupied by
crested wheatgrass, the model assesses the probability of
invasion to each neighbor whose edge-to-edge distance is
# 100 m. For each source–neighbor pair, the model
determines the potential spread distance and compares it
to the centroid-to-centroid distance for the pair. We used a
Pareto distribution (Equation 1) of annual spread distances
for modeling short and intermediate spread distances (1 to
100 m). The long tail of the distribution captures the
observation that most seeds disperse within a short distance
of a source patch, but that some proportion of seeds may be
transported a considerable distance.
Decision Tree. Our five management strategies and three
uncertainty components resulted in 36 possible simulations
of the model (Electronic Appendix). Each simulation was
replicated twice for a total of 72 model runs. Due to the
multifactorial nature of the experimental design, there are a
total of 36 replicates for each alternative hypothesis about
crested wheatgrass short- and long-distance dispersal rates,
and 32 replicates for each alternative hypothesis about
control effectiveness. Each management strategy was
replicated 16 times, and the inaction strategy was replicated
8 times. For each simulation, the expected outcome is
calculated as the product of the mean outcome, and the
probabilities assigned to the hypotheses assumed for that
simulation. For each strategy, the sum of its probability
products adds to one, and the expected outcome is
calculated as the sum of the expected outcomes for each
combination of hypotheses possible. Initially we assigned
each alternative hypothesis for our management strategies
equal probabilities.
Sensitivity Analysis. We conducted a sensitivity analysis
using the probabilities assigned to alternative hypotheses
across the full three-dimensional probability space for
rate of patch spread, rate of long-distance dispersal events,
and control effectiveness. This allowed us to identify
strategies that are robust to uncertainty in these compo-
nents and to identify data gaps that are critical for our
ability to predict which management strategies are the most
effective.
Performance Measures. We examined two model outputs
from each simulation that were relevant for our questions:
the cumulative area treated in the invaded and established
states over a 50-yr period and the integral of the area
invaded over time in each state. Because the state of every
polygon was only printed every ten time-steps, the area
covered by crested wheatgrass over time was linearly
interpolated. We assumed that the percent of a polygon
covered by crested wheatgrass was 30% in the invaded and
90% in the established states.
Results and Discussion
The cumulative area covered by crested wheatgrass over
the 50-yr simulation period varied by a factor of nine, from
6,141 ha for the large-patch–first strategy, with twice the
current budget under the hypotheses of effective control,
slow spread, and few satellites, to 53,568 ha for the
inaction strategy under the hypotheses of fast spread and
many satellites (Table 1). The cumulative area treated over
the 50-yr simulation period ranged from 0 ha under the
inaction scenario to 2,675 ha for the large-patch strategy,
with double the current budget under the fast-spread and
many-satellite hypotheses.
Differences in outcomes between the two management
strategies were clear (Figure 3). While the early detection
and control scenario (Figure 3b) eliminates all small
330 N Invasive Plant Science and Management 2, October–December 2009

8. patches and reduces the total number of patches, but leaves
several very large patches on the landscape, the strategy that
prioritizes the largest patches (Figure 3c) reduces their size,
but results in many more patches overall.
Parameter Sensitivity. The strategies that treat larger areas
result in less crested wheatgrass remaining after 50 yr in our
simulations (Figure 4). However, it takes fewer small-patch
treatments to achieve equivalent effectiveness to the large-
patch treatment program. To understand the implications
of uncertainty with respect to the probability assigned to
these hypotheses, we conducted a sensitivity analysis for the
full three-dimensional probability spaces for the inaction
simulations (Figure 5), and for the four simulations in
which treatments were applied (Figure 6). In the absence of
any treatment, the average annual coverage of crested
wheatgrass in the park over a 50-yr period ranges from 920
to 1,060 ha (Figure 5). Most of the variation in this range
is explained by the probability assigned to the fast- vs. slow-
patch spread hypothesis, whereas varying the probability of
long-distance dispersal events had very little effect on
crested wheatgrass cover after 50 yr.
Note that the many new patches setting sometimes
results in a lower cumulative area invaded over the course
of the simulation (Table 1). This is true in 33% (6 out of
18) of all possible pair-wise cases where all other parameters
are equal. The reason this occurs is because we are using a
stochastic simulation model based on probability distribu-
tions, not a deterministic model. At each time-step, the
model draws from a Poisson distribution to determine the
number of new patches from outside of the landscape that
will be initiated in the study area. For the many new-
patches hypothesis we used a higher number (2) as the
average for the distribution vs. (1) for the few-patch
hypothesis. However, given the stochastic nature of the
process in some time-steps, there could be a large number
of new patches for the few-patch hypothesis or even zero
patches under the many-patch hypothesis. Additionally,
there are other stochastic processes occurring during the
simulations, including control success rates and spread
Figure 3. Sample spatial outputs for a portion of the park known
as Larson Block in year fifty of three simulations. Crested
wheatgrass infestations are shown in black. Results shown are for
the most pessimistic assumptions (fast spread, many satellites,
and low control effectiveness). Strategies shown are (A) inaction,
(B) current capacity prioritizing early detection and control of
new patches, and (C) current capacity prioritizing the control of
large existing infestations. Long linear infestations occur along
road rights-of-way.
Figure 4. Simulated outcomes of average crested wheatgrass area
and total treatments over 50 yr for Grasslands National Park,
assuming equal probabilities for all alternative hypotheses of
spread rate, control effectiveness, and satellites. Strategies are
inaction (No-MGT), prioritize large-patch edges (LPE), and
prioritize the smallest patches (SP). Annual control budgets are
either 50 or 100 polygon ha/yr (124 to 248 ac/yr).
Frid and Wilmshurst: Crested wheatgrass decision analysis N 331

9. distances that could result in higher cumulative area
invaded for the few-patch hypothesis. For the majority
of the simulations (66%), the many-patch hypothesis
has greater cumulative area invaded: and, on average, there
is 1.5% more area invaded with the many-patch
hypothesis.
Our decision analysis demonstrated the interaction
between control effectiveness and control strategy on the
ability to manage crested wheatgrass invasions in our
scenario landscape (Figure 6). When budgets are sufficient
to treat 100 ha of invaded crested wheatgrass per year, the
probability that the large-patch or small-patch treatments is
the highest ranked strategy changes as a function of control
effectiveness. The highest ranking strategy shifts gradually
from the focus on small-patch control when control
effectiveness is low, to large-patch control when control
effectiveness is high (Figure 6). When budgets are
sufficient to control only 50 ha of crested wheatgrass per
year, control effectiveness has no effect on rank, with small-
patch focus always ranking better than the large-patch
strategy (Table 1).
The Role of Control Effectiveness in Control Strategy. Control
effectiveness has the most complex effects on the overall
area treated in a control program (Figure 6). Treatment of
50 ha of small patches of crested wheatgrass per year ranks
first for all values of control effectiveness below 100%.
Between 80 and 100% effectiveness, annually treating
50 ha of small patches slips to third in terms of cost behind
small-patch and large-patch treatment of 100 ha/yr.
Similarly, annual treatment of only large patches totalling
50 ha annually declines from second to fourth rank,
between 60 and 100% control effectiveness. The best
strategy for controlling crested wheatgrass while treating
the smallest area is only sensitive to changes in control
effectiveness when that effectiveness is at or close to 100%.
Figure 5. Average crested wheatgrass coverage (ha) over 50 yr
with no management as a function of the probability assigned to
the fast-spread hypothesis and the many-satellite hypothesis.
Figure 6. The best strategy for reducing crested wheatgrass cover (top row of panels) and minimizing area treated (bottom row of
panels) is displayed with respect to the probability assigned to the effective-control hypothesis (columns). Within each panel, the
probabilities assigned to the many-satellite hypothesis and the probability assigned to the fast-spread hypothesis are shown as in
Figure 5. The probability of many satellites varies along the x-axis, while the probability for fast spread varies along the y-axis. Each
major column of panels represents a point in probability space for effective control. Probabilities for the complementary alternative
hypotheses (ineffective control, few satellites, slow spread) are equal to one minus the probability shown in the figure. The strategy that
resulted in the least area covered by crested wheatgrass over time, or the least area treated, is labelled and shaded within the region of
parameter space. Strategies use either the revegetation plan for restoration (50 polygon ha (124 ac) of treatments per year) or twice that,
and prioritize either early detection and control of new infestations (SP), or reduction in the size of large known infestations (LPE).
Strategy rankings for all parameter combinations are provided in the supplemental material.
332 N Invasive Plant Science and Management 2, October–December 2009

10. With a program that has both a large budget and
effective control, it is possible that control efforts will not
be overwhelmed by spread from large patches. Doubling
the current capacity for treatment can shift strategy
rankings such that prioritizing large existing infestations
ranks first, but only under conditions in which control is
highly effective or when spread is slow and the rate of
appearance of new infestations is high. This cannot be
sustained if the effectiveness of control effort is low.
Wadsworth et al. (2000) showed that under conditions in
which long-distance dispersal is the dominant form of
dispersal, it is better to prioritize larger patches. Our results
are in agreement with this conclusion.
Our results suggest an interaction between control
effectiveness and patch size. The biology of crested
wheatgrass suggests that monitoring and control of small
patches should be adopted as a priority by land managers,
largely because of the relative infrequency of long-distance
dispersal. While seed production of crested wheatgrass is
high (Heidinga and Wilson 2002; Pyke 1990) most seeds
disperse short distances (Marlette and Anderson 1986).
Indeed, what is more striking with crested wheatgrass is its
temporal pattern of dispersal. Seeds are released from the
flowering culm over an extended period of time (Pyke
1990) and can remain resident in the seedbank for 4 yr or
more (Wilson and Pa¨rtel 2003). Hence, crested wheatgrass
tends to form virtual monocultures in which there is a
strong positive relationship between plant cover and
seedling density (Marlette and Anderson 1986). This
means that attempts to control an established infestation of
crested wheatgrass may be overwhelmed by its ability to
reestablish within large infestations. While this does not
mean that small infestations are easy to control, it suggests
that control effectiveness may be inversely related to patch
size, with greater control efficiency on a strategy that targets
smaller patches.
Some studies have shown that increased short-term
funding can reduce the overall long-term expenditure of
funds for controlling invasive weeds (Higgins et al. 2000b;
Taylor and Hastings 2004). In our simulations, this is only
true under conditions in which control efforts are highly
effective. Under these conditions, increased short-term
capacity can reduce levels of crested wheatgrass quickly
enough that the required level of effort subsequently
decreases steadily over time. Otherwise, under conditions
of imperfect control, doubling of current capacity always
results in greater expenditures over the 50-yr period. Land
managers are therefore faced with a trade-off: do they trust
that long-term control is highly effective (Wilson and
Pa¨rtel 2003) and allocate more resources to crested
wheatgrass control, foregoing other long-term priorities,
or do they maintain levels of treatment at current capacity
and potentially tolerate greater levels of crested wheatgrass
within the landscape over the long term? Research to both
measure and improve control effectiveness will help resolve
this impasse and may result in a clearer set of decisions.
The Role of Financial Constraints on Control Strategy. In our
model simulations, the trade-off between short- and long-
term control was resolved in part by the financial realities
of invasive species management. In the absence of a budget
sufficient to entirely control large crested wheatgrass
patches, the best strategy was always to focus resources
on small patches (Table 1). Regardless of how effective
crested wheatgrass control may be, a budget that is
insufficient to control large patches constrains the manager
to focus on small patches. This occurs because attempts to
control large patches without adequate resources to do so
comprehensively are always overwhelmed by the capacity of
the patches to spread. Under these conditions, allocating
resources to early detection and control of new infestations
always ranks better, both in terms of total area treated over
50 yr and in terms of the average area covered by crested
wheatgrass over this time period.
Our results show that under current levels of funding
and uncertainty, the strategy that most often ranks best
towards reducing the coverage of crested wheatgrass is one
of early detection and control of new infestations, as has
been recommended by Simberloff (2003). This result is
consistent with the conclusion drawn by Moody and Mack
(1988): that ignoring nascent foci results in more large
patches in the future, and that focusing treatments on large
patches may be ineffective because spread from theses
patches tends to overwhelm control efforts.
While our simulations considered a base budget that
allows for 50 ha of restoration per year as outlined in the
revegetation plan for Grasslands National Park, the actual
budget levels in recent years that are allocated to restoration
are far lower, in the order of only 6 to 12 ha of CWG
restoration per year. If land managers wish to consider
increasing the capacity for treatment, there are some key
uncertainties that must be resolved to determine whether
management should prioritize early detection and control
of new infestations, or reducing the size of large existing
infestations. As already stated, if control efforts are highly
effective and budgets are high then allocating resources to
large existing infestations always ranks better than
prioritizing early detection and control of new infestations.
Research into the effectiveness of control efforts has been
conducted at Grasslands National Park for over a decade
(Ambrose and Wilson 2003; Bakker and Wilson 2004;
Wilson and Pa¨rtel 2003; Wilson et al. 2004), but always in
small plots (# 30 m2
). This has guided the park’s current
management actions (Sturch 2005), but understanding of
control effectiveness in large-scale restorations (# 50 ha)
over the long-term is still poor. Consideration of control
effectiveness appears to be restricted to invasive species
control simulation models (Eiswerth and Johnson 2002;
Frid and Wilmshurst: Crested wheatgrass decision analysis N 333

11. Leung et al. 2002; Rinella and Sheley 2005; Shea and
Kelley 2004), and has not become a consideration that field
studies are commonly reporting, despite its importance for
decision making. If control efforts are not effective, then
other key uncertainties are the rates of patch spread and
long-distance dispersal. Rates of patch spread have been
measured in Grasslands National Park (Hansen 2006;
Henderson 2005), but rates of long-distance dispersal have
not, owing in large part to the expense of establishing a
sampling protocol that has sufficient power to detect long-
range dispersal events.
Our analysis first assumes that the ranges assigned to
parameters for alternative hypotheses about spread and
control are representative of the full plausible range of
possibility for these parameters, and secondly, that
detection of new patches is relatively inexpensive. It is
important to verify that the values of our parameters are
within plausible ranges even if managers are not consid-
ering an increase in current capacity. For example, the
average number of new infestations in the park, modelled
with the Poisson distribution, was based on very little
available information. One possible approach to improving
this would be to establish long-term sampling areas for new
infestations that are distant from any existing sources. The
rate at which new infestations appear in these areas could
be used to inform the long-distance–spread-parameters
used for future simulations. Such a monitoring program
would have the additional benefit of detecting new
infestations early enough that the cost of treating them
would be low. If detecting new infestations is expensive and
requires a great deal of resources, it may be more effective
to focus on patches that are already known. However, as
noted in our description of control costs, it is much more
expensive to control large vs. small patches because of the
requirement for seeding. Using real monitoring costs as a
guide, an observation model that explicitly considers the
tradeoffs between monitoring and treatments could be
developed. This also reinforces the need for practitioners to
improve their knowledge on control effectiveness with
every control program they implement.
Structured Decision Analysis. It is in managing the key
uncertainties and assumptions that the formal process of
decision analysis plays a useful role. Decision analysis has
two elements: a probability model that assigns probabilities
to uncertain (biological) events, and a values model that
weighs the costs and benefits to all parties of the range of
possible actions recommended by the probability model
(Maguire 2004). Hence, decision analysis acts as more than a
population model by incorporating a cost to stakeholders of
management activities, affecting how priorities are set in a
complex management environment (Drechsler and Burg-
man 2004; Ellison 1996). In our case, the values of the park
managers are well understood by all stakeholders, and
actions to control crested wheatgrass have predominantly
economic costs with few values conflicts. Nevertheless,
crested wheatgrass continues to be seeded and cultivated as
an important hay crop all around the park. Thus, it is clear
that if control efforts by land managers for crested
wheatgrass were to attempt to extend beyond the park
boundary, our ‘‘values’’ landscape would become consider-
ably more complex and hence would alter decision making.
This model is a first approximation to our description of
the problem. Subsequent to this analysis we have identified
four shortcomings and identified future analyses that would
improve the level of confidence in our results. First, the
transition between the initial and established states is
artificial, and there is more likely a gradual continuum
between a polygon with a single crested wheatgrass plant
and one that has 100% cover of crested wheatgrass. The
complete transformation of the community is somewhat
compensated for by a minimum residence time of 10 to
15 yr in the invaded state before transition to the
established state was possible. A second shortcoming is
that it is difficult to relate control effectiveness parameters
back to monitoring data on control effectiveness. Control
effectiveness parameters that are easier to quantify would
make it easier to relate to the percent reduction in crested
wheatgrass cover on a polygon. Third, our treatment
budgets are simulated in terms of polygon area, rather than
the absolute coverage of crested wheatgrass. Coverage of
crested wheatgrass varies according to state, but this can not
be incorporated into our budget ceilings for treatments. A
better approach would incorporate a percent cover
relationship per ha against time since invasion. Treatment
ceilings would then be applied against total area covered by
crested wheatgrass rather than polygon areas. Reductions in
cover from different levels of control effectiveness would
lead to setting back the age-cover relationship. Finally, we
do not explicitly consider costs and limitations on
monitoring efforts. This could be incorporated in a state
and transition formulation in which crested wheatgrass is
present but unknown, or present and known, to managers.
Monitoring efforts could be incorporated into the state-
change rules that transition polygons from unknown to
known states, assuming different detection probabilities.
Our decision analysis approach to the management of
invasive plants would be well suited to a broader adaptive
management framework (Shea et al. 2002) because it
explicitly deals with uncertainty and makes predictions
about the performance of alternative management strategies
under different hypotheses. As an example, managers could
subdivide the affected landscape into different experimental
units and use alternate strategies in each. Monitoring of
crested wheatgrass population densities and locations
within each unit would help determine if our predictions
regarding the most effective management strategies really
are correct.
334 N Invasive Plant Science and Management 2, October–December 2009

12. Measurements of parameters conducted within each unit
would enable us to improve our model and increase our
confidence in future decisions. Based on these experimental
results, both the parameter ranges chosen and the
probability space used for sensitivity analysis could be
refined. Accurate information on control effectiveness was a
key uncertainty in our model, and this can best be
improved in a managed setting using adaptive management
approaches.
There are various situations under which adaptive
management may not be possible, including lack of
resources, long response times, difficulty monitoring, and
others (Shea et al. 2002). Indeed, there can be more to
characterizing consequences and analyzing cost-benefit–
trade-offs than the suite of variables we have used. In this
case, decision analysis will not reduce uncertainty, but can
at least identify the most effective strategies to pursue until
more information or resources become available. This was
the case with crested wheatgrass, where we found that
under current budget levels and the parameter ranges we
identified, a strategy of directing control efforts at detecting
and treating new patches is always better than focusing on
large known infestations.
Sources of Materials
1
VDDT, Vegetation Dynamics Development Tool. Available for
download at http://www.essa.com/downloads/vddt/download.htm.
2
TELSA, Tool for Exploratory Landscape Scenario Analyses.
Available for download at http://www.essa.com/downloads/telsa/
download.htm.
Acknowledgments
This work was supported by the Parks Canada Species at
Risk Recovery and Education Fund, Grasslands National Park
of Canada, and ESSA Technologies Ltd. We thank Russ
Walton for thoughtful comments on the initial model design.
Kelly Robson provided assistance in the preparation of the
figures. Two anonymous reviewers, Donald Robinson, Darcy
Henderson, and Judy Toews reviewed an earlier version of the
manuscript.
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Received February 16, 2009, and approved July 28, 2009.
336 N Invasive Plant Science and Management 2, October–December 2009