frid and wilmshurst 2009

Decision Analysis to Evaluate ControlStrategies for Crested Wheatgrass

(Agropyron cristatum) in GrasslandsNational 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, ecosystemservices and human activities globally (Mooney 2005).Significant resources are expended around the world on theprevention of new invasions and on the control of existingones (Perrings et al. 2005). While at a small scale controlefforts can be highly effective, for the most part, managersattempting to control invasive plants at landscape scales arefighting losing battles (Rejmanek et al. 2005). Failure ofcontrol efforts at large spatial scales is, in part, driven by

our lack of species and landscape specific informationabout the distribution and spread of the invaders (Shea andChesson 2002). Unfortunately, this type of information isdifficult to obtain and requires precious time that is thenlost for control efforts. Land managers require tools thatallow them to choose the most suitable managementstrategy to control invasive species in the face ofuncertainty. One such tool, decision analysis, can be usedto rank alternative management decisions (Clemen 1996;Peterman and Anderson 1999). Decision analysis iscommonly used in fields such as fisheries management(Alexander et al. 2006; Peters and Marmorek 2001; Peterset al. 2006) but there are few examples of its use in invasivespecies management (Maguire 2004). Here we presentdecision analysis as a tool in invasive species managementplanning through the example of crested wheatgrass[Agropyron cristatum (L.) Gaertn.] in Grasslands NationalPark.

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: [email protected]

Invasive Plant Science and Management 2009 2:324–336

324 N Invasive Plant Science and Management 2, October–December 2009

Crested wheatgrass was introduced into the NorthAmerican Great Plains from Eurasia in the 1800sand gained importance as a forage crop for grazing andhay in the 1930s (Dillman 1946; Henderson 2005; Roglerand Lorenz 1983). While the popularity of crestedwheatgrass as a crop continues, its propensity to invadeundisturbed rangeland (Hull and Klomp 1967; Marletteand Anderson 1986), particularly east of the continentaldivide (Henderson 2005), makes it an undesirablespecies in communities where the preservation of nativegrassland is a management objective. This is the case inGrasslands National Park, Saskatchewan, Canada, wherecrested wheatgrass spreads from hay fields, pipelines, androad rights-of-ways into surrounding native mixed-grassprairie.

Natural area managers and researchers have worked foryears to determine the best methods to stop crestedwheatgrass encroachment (Bakker et al. 1997; Bakker andWilson 2001; Christian and Wilson 1999; Hansen 2007;Hansen and Wilson 2006; Henderson 2005) and restoreinvaded areas (Ambrose and Wilson 2003; Bakker andWilson 2004; Parks Canada Agency 2002; Sturch 2005;Wilson et al. 2004). These efforts have provided valuableinformation on the invasion biology of crested wheatgrassand have resulted in methods of control and restorationthat 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 nativevegetation, is only the first step in managing this ecosystem.A strategy is needed to control crested wheatgrass spreadand decrease its cover at landscape scales over long timeperiods.

Given limited financial resources, crested wheatgrasscontrol will take years, and likely decades, so a strategy that

maximizes the long-term effectiveness is required. Ourobjective is to determine how land managers can bestallocate limited funds for crested wheatgrass control andrestoration, to provide the greatest and fastest reduction incrested wheatgrass cover over the next 50 yr.

One of the first decisions that must be made whenallocating limited resources to the control of invasive plantsis whether to focus on known existing large infestations oron finding and controlling inconspicuous small nascentfoci. Moody and Mack (1988) showed that under certainconditions it is more effective to prioritize small nascentfoci for management, but Wadsworth et al. (2000) foundthat this may not be the case for plants that spread mainlyby long-distance dispersal. These two findings highlight theneed for a detailed understanding of the natural history ofinvasive species to enable managers to make decisions ontreatment priorities.

Managers must also decide how many resources todevote to invasive management. Various studies haveshown that spending less in the short term can bemore costly in the long term (Higgins et al. 2000a;Pimentel et al. 2000). However, allocating more resourcesto controlling invasive plants is almost always at theexpense of other management priorities, underscoring theneed for an ecological cost-benefit analysis to justifysignificant expenditures (Andersen et al. 2004). It istherefore important to evaluate the relative long-termbenefits of making these short-term sacrifices (Taylor andHastings 2004).

To protect the remaining tracts of native mixed-grassprairie, ecologists from Grasslands National Park arecurrently considering a variety of alternative actions intheir 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 longterm; second, should control and restoration focus onemergent or established infestations; and finally, howshould the effort be partitioned between monitoring,control, and restoration? These decisions must be madein the face of uncertainty in three key components of thesystem: (1) the effectiveness of restoration and controlefforts, (2) the rate of spread of existing patches, and (3) therate of increase in newly infested, initially small patches. Toaid decision making and to identify knowledge gaps in ourunderstanding of the invasive biology of crested wheatgrass(Byers et al. 2002) we developed simulation models toreflect both management actions and alternative hypothesesabout the dynamics of crested wheatgrass spread andcontrol. We then applied the technique of decision analysis(Clemen 1996; Ellison 1996; Peterman and Anderson1999; Peterman and Peters 1998) to analyze our modelresults and rank management alternatives for crestedwheatgrass given uncertainty.

Interpretive SummaryThe decision analysis approach integrates biological, economic,

logistical, and, if relevant, sociological information and constraintsto meeting any management challenge. The challenge is to gatherrelevant data on these disparate elements to apply to the model.Much of this can be gathered using the principles of adaptivemanagement. By keeping track of successes, failures, and the costsof implementing alternative control strategies, sufficientinformation will be available for a formal decision analysisprocess. However, the key is to consider alternatives. Theinformation we present through this example is appropriate toany invasive plant management problem that involves decisionsabout resource allocation and alternative strategies, as well asuncertainty about the underlying dynamics of the natural andmanagement systems. We suggest that rather than adopting an ad-hoc approach to invasive plant management by following thestatus quo or applying rules of thumb, managers should explicitlyconsider uncertainty and challenge alternative managementstrategies by following a decision analysis approach.

Frid and Wilmshurst: Crested wheatgrass decision analysis N 325

Materials and Methods

Study Area. Grasslands National Park (42,368 ha,49u159N, 107u09W) was established in 1988 to preservea representative portion of the Canadian mixed-grassprairie ecosystem (Figure 1). The climate is consideredsubhumid; winters are long, cold, and dry, while summersare short and hot. Mean daily temperature ranges from15 C below zero in January to 20 C (68 uF) in July. Totalannual precipitation averages 325 mm (12.8 in), with mostfalling as rain in the spring months, and approximatelyone-third falling as snow in the winter. The growing seasonin the park is relatively short, averaging 170 d betweenkilling frosts, but low moisture availability often reduces itslength further (Loveridge and Potyondi 1983).

We subdivided the park into five biophysical units basedupon the vegetation inventory of the park (Michalsky andEllis 1994): upland grassland, sloped grassland, valleygrassland, shrub communities, and eroded communities.Crested wheatgrass can be found in all of these biophysicalunits. While it has been seeded as a hay crop in the uplandand valley grasslands, and in some cases the shrubcommunity (the riparian zone in the park), it has spreadinto the sloped grasslands and eroded communities.

Decision Analysis Framework. We calculated the conse-quences of alternative management strategies to controlcrested wheatgrass, probability weighted by our alternativehypotheses for the rate of spread, the effectiveness ofcontrol, and the rate at which new patches appear on thelandscape. Our decision analysis had six components: (1)alternative actions, (2) performance measures, (3) uncer-tainties related to the dynamics of crested wheatgrass spreadand control, (4) a model to predict outcomes, (5) adecision tree, and (6) sensitivity analyses. Each of thesecomponents is described below.

Alternative Actions. We considered alternative strategiesbased on four possible combinations of two managementcomponents: the annual budget allocated to crestedwheatgrass treatment (high or low) and the prioritizationstrategy of treating large existing patches vs. small newpopulations. Two alternative budgets were expressed as aceiling on the annual area that could be treated. Therevegetation action plan for the park sets a goal of 45 to65 ha/yr (111 to 161 ac) of restoration in the park (Sturch2000). The budget alternatives represent the revegetationaction plan (50 ha/yr), and a doubling of the area allocatedfor 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.


1 ha. For large patches, the cost of restoration is about$1,200 Canadian (Cdn)/ha, which includes the cost ofchemical treatment ($60), native seed ($1,100), equipmentand labor ($40). Therefore, our budget alternativesrepresent annual expenditures of approximately $60,000and $120,000 Cdn annually for the low and high budgetscenarios, respectively. The cost of treating the smallpatches is considered to be much lower (approximately$100/ha) because heavy equipment and native seed is notrequired. At this rate, treating 50 ha of small new patchesonly 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 ofmonitoring for small new patches per year under the lowbudget scenario. Thus, our alternative strategies considerthe trade-off between applying all available resources tocontaining large known infestations vs. investing someresources in early detection in order to control small newinfestations before they become established. As a bench-mark we also considered inaction (no treatment) as ahypothetical alternative.

Performance Measures. The performance measures weused to evaluate each combination were (1) the cumulativearea treated over a 50 yr period as an indicator of the totalcost of each treatment strategy, and (2) the cumulative areacovered by crested wheatgrass over that period, as anindicator of the outcome of each management strategy. Wechose the cumulative area invaded by crested wheatgrass,the sum of the area of the park covered by crestedwheatgrass each year across all years, rather than simply thefinal area at year fifty to track both the rate and magnitudeof change in crested wheatgrass cover over time. Modelresults are reported as area treated and cumulative areacovered by crested wheatgrass over the simulation timeperiod.

Uncertainties. We focused our analysis of uncertainty onwhat are perceived to be three key unknowns in crestedwheatgrass dynamics. These are (1) the rate at whichpatches spread across the landscape over time, (2) the rateat which new patches appear via long-distance dispersal,and (3) the effectiveness of site-specific control efforts.

The invasion of crested wheatgrass follows two distinctpatterns. The first is the expansion of hay field margins.Fields of crested wheatgrass generally spread into the nativeprairie along their windward margin via seed dispersal(Hansen 2006). Crested wheatgrass produces prodigiousamounts of seed (Cook et al. 1958; Pyke 1990) and theseed establishes readily, accounting for its popularity as ahay crop (Rogler 1954). This seed is wind dispersed shortdistances by rolling over hard ground or snow, resulting ina field that can creep upwards of 1 m/yr from a seeded fieldmargin (Ambrose and Wilson 2003; Henderson 2005).The shape of the dispersal kernel of crested wheatgrass is

known from only a few unpublished studies (DarcyHenderson, personal communication). Recent work inthe Canadian prairie has successfully used a hyperbolicPareto distribution to model seed dispersal for invasive wildoats (Avena fatua L.) (Shirtliffe et al. 2002). We also usedthe Pareto distribution to model the dispersal kernel forcrested wheatgrass (Equation 1).

P Spreadvxð Þ~1{xm

x

� �a

½1�

where xm, the minimum spread distance, is set at 0.5 m(Henderson 2005) and a is the shape parameter. Becausewhat is most important about a dispersal kernel is not itsmean distance but the shape of its tail (Clark and Fastie1998), we modeled fast spread using a fat-tailed dispersalkernel (a 5 2.01) and a slow spread using a narrow-taileddispersal kernel (a 5 3). The mean annual spread distancebetween 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 of2.08. The mean spread rates are within the range of whathas been observed (Henderson 2005), but there isuncertainty around the shape of the distribution.

The second form of spread is the long-distance dispersalof crested wheatgrass seed, likely in herbivore dung. Thisform manifests itself as satellite plants or small patchesappearing far distances from the nearest seed source. Theseplants, which can be found in every vegetation communityin the park, become a seed source for short-distancedispersal. As a result, unexpected patches of crestedwheatgrass can appear in otherwise undisturbed areas ofthe park, and left unmanaged, these can grow to becomelarge invaded areas. While these are routinely observed inthe park, we only have limited information about the rateat which these new patches of crested wheatgrass appear.Therefore we set two rates: many (average of two newsatellites per year) and few (average of one new satellite peryear) (Table 1, electronic appendix). The actual number ofnew infestations in the park was modeled using the Poissondistribution with mean values of 1 and 2 to differentiatebetween many and few satellites.

The effectiveness of control efforts is another factor thatis considered highly uncertain. While recent restorationresearch has provided the park with effective tools foreliminating crested wheatgrass (Bakker and Wilson 2004;Hansen and Wilson 2006; Sturch 2005; Wilson and Gerry1995; Wilson and Partel 2003), there is still variability inthe effectiveness and persistent benefit of these techniques.Based upon experience in the park, control effectivenesscan vary between complete elimination of crested wheat-grass, to setting the crested wheatgrass back such that itpersists but does not spread (effective), to failure, in whichspread continuous unabated (ineffective). Hence, we variedthe probabilities of these outcomes for two levels of relative


control effectiveness (effective and ineffective) for newcrested wheatgrass infestations.

Model. We developed a spatially explicit simulation modelto compare the different landscape level control strategiesand to determine the sensitivity of each strategy touncertainty 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 andcontrol at a 1 ha scale, and second, a spatially explicitspread model that considers how crested wheatgrass arrivesat uninvaded areas from within invaded areas or fromoutside of the modeled landscape.

We developed our state and transition models using TheVegetation Dynamics Development Tool (VDDT).1

Table 1. Simulation results for all 36 possible combinations of strategy and hypotheses for control effectiveness, spread rates, andsatellite 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 apolygon to transition into the established state after invasion. Few and many satellites are modelled as Poisson mean values of 1 and 2respectively 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]


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]


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]


Slow Many 25,823 [63,809] 1,419 [3,506]Few 25,770 [63,678] 1,437 [3,550]


VDDT is a software tool for creating and simulating semiMarkovian state and transition models (ESSA TechnologiesLtd. 2005b). VDDT has been used to simulate variousecosystems including the dynamics and restoration ofsagebrush steppe communities (Forbis et al. 2006), historicfire regimes across the continental United States for theLANDFIRE project (Anonymous 2009) and others(Arbaugh et al. 2000; Hemstrom et al. 2001; Merzenichand Frid 2005; Merzenich et al. 1999).

Models developed in VDDT outline the possiblevegetation states of the landscape as well as transitionsbetween states. These transitions are either deterministicand occur after a fixed period of time, or stochastic, havinga given probability of occurring each annual time-step.VDDT models are simulated numerically and track boththe state of the landscape over time as well as theoccurrence of transitions.

The model we developed for crested wheatgrass consistsof three possible states: uninvaded, invaded, and established(Figure 2). The uninvaded state represents a polygon inwhich crested wheatgrass is absent. From this uninvadedstate, a polygon can transition to the invaded state throughinvasion either by spread from a neighboring polygon thatis invaded, or by long-distance dispersal. The invaded staterepresents a polygon that has detectable levels of crestedwheatgrass, but in which other plant species are stilldominant. Polygons in the invaded state act as weaksources of crested wheatgrass to neighboring polygons.Management efforts applied to crested wheatgrass ininvaded polygons frequently result in control, returningthe polygon to the uninvaded state. Occasionally, manage-ment efforts may reduce the cover of crested wheatgrass in apolygon without accomplishing a transition back to theuninvaded state. It is also possible that if management isapplied incorrectly or under the wrong environmentalconditions, there will be no effect on the state of thepolygon. If enough time elapses in the invaded statewithout effective management, a polygon will transitioninto the established state. Under the fast-spread hypothesiswe set the time to transition to the established state at10 yr, vs. 15 yr for the slow-spread hypothesis. Thesevalues were set based on personal communications withmanagers at the park.

The established state represents a polygon in whichcrested wheatgrass is the dominant vegetation type.Polygons in this state act as strong sources of crestedwheatgrass to neighboring polygons. Management effortsapplied to crested wheatgrass in the established state rarelyresult in control back to the uninvaded state, but mayfrequently result in the reduction of enough cover totransition a polygon from the established to the invadedstate. However, the failure of management efforts to haveany impact in the established state is also relativelyfrequent.

By itself, the state and transition model shown in Figure 2is not spatially explicit and describes only the dynamics ofcrested wheatgrass within each 1 ha polygon. We simulatedthe spread of weeds among polygons in our five biophysicalunits using the Tool for Exploratory Landscape ScenarioAnalyses (TELSA).2 TELSA was developed to simulatelandscape-level terrestrial ecosystem dynamics over time, toassist land managers in assessing the consequences of variousmanagement strategies (Beukema et al. 2003; ESSATechnologies Ltd. 2005a; Kurz et al. 2000).

For this study, the inputs for our TELSA simulations ineach landscape include1. state and transition models (Figure 2) for the five

vegetation communities in the landscape2. spatial, geographic information system (GIS) data layers

representing vegetation communities and the currentcrested wheatgrass distribution of the landscape

3. parameters governing the spatial spread and control ofcrested wheatgrass (These parameters include theprobability distribution of neighbor-to-neighbor spreaddistance at each annual time-step and the averagenumber [Poisson] of new infestations from outside thelandscape at each time-step.)Input polygons defining the initial state and vegetation

community of the landscape are subdivided into simulationpolygons through a process called ‘‘Voronoi Tessellation’’(Kurz et al. 2000). Unlike the use of a grid, this processdivides original polygons into smaller units for simulationwithout losing any of the original boundary information.While computationally more demanding, the resolution offeatures that are important for weed spread, such as riparianand transportation corridors, is maintained. We used49,602 simulation polygons with an average size of 0.85 60.001 ha (mean 6 standard error [SE]).

The creation of new infestations depends upon therelative probability that any polygon in the park could beinvaded by crested wheatgrass via long-distance dispersal,

Figure 2. State and transition model for crested wheatgrassdynamics. Invasion is a stochastic process influenced byproximity to neighboring infestations and vegetation communi-ty. Escape to an established infestation occurs after 10 to 15 yr ofinaction. Control efforts can set back population densities ofcrested wheatgrass, eradicate the population, or fail to haveany effect.


which is a function of the vegetation community withinwhich it resides. Based on random sampling in the park,Hansen (2006) reported the area of crested wheatgrassinvasion in vegetation communities in Grasslands NationalPark. We converted these to proportional vulnerabilities,and using these proportions, ranked invasion susceptibility(from most to least invaded) as valley grassland, shrubcommunity, sloped grassland, upland grassland, anderoded community. Given that most of our crestedwheatgrass source communities are in valley grasslands,our probabilities are calculated relative to the valleygrassland landscape position. Based on these rankings, therelative susceptibility of each of these communities tocrested wheatgrass invasion is valley grassland 1, slopedgrassland 0.68, shrub community 0.68, upland grassland0.59, and eroded community 0.18 (Hansen 2006). These,then, are the relative probabilities that each of thesecommunities in the simulations would be invaded by long-distance dispersal; probabilities that also serve to scale therelative rates that these communities are invaded by short-distance dispersal. For example, if there were equal areas ofvalley grassland and upland grassland in the landscape, a newlong-distance dispersal event would only be 59% as likely tooccur in the upland grassland as in the valley grassland. Forshort-distance dispersal, spread into the upland grasslandwould be on average only 59% as far as into the valleygrassland. For simulating long-distance dispersal, we usedthe Poisson distribution to describe the number of newpatches of crested wheatgrass appearing in the park annually.As alternatives, we modeled long-distance dispersal as meannumbers of new patches being equal to one or two per year.These we identify in the text as few or many patchesrespectively. Given that there is no information available onlong-distance patch establishment for crested wheatgrass, wechose these values as they spanned a reasonable range ofpatch densities in model simulations. We will discuss theimplications of altering these values.

After the simulation of new infestations, the modelsimulates the expansion of existing infestations betweenadjacent polygons. For each polygon already occupied bycrested wheatgrass, the model assesses the probability ofinvasion to each neighbor whose edge-to-edge distance is# 100 m. For each source–neighbor pair, the modeldetermines the potential spread distance and compares itto the centroid-to-centroid distance for the pair. We used aPareto distribution (Equation 1) of annual spread distancesfor modeling short and intermediate spread distances (1 to100 m). The long tail of the distribution captures theobservation that most seeds disperse within a short distanceof a source patch, but that some proportion of seeds may betransported a considerable distance.

Decision Tree. Our five management strategies and threeuncertainty components resulted in 36 possible simulations

of the model (Electronic Appendix). Each simulation wasreplicated twice for a total of 72 model runs. Due to themultifactorial nature of the experimental design, there are atotal of 36 replicates for each alternative hypothesis aboutcrested wheatgrass short- and long-distance dispersal rates,and 32 replicates for each alternative hypothesis aboutcontrol effectiveness. Each management strategy wasreplicated 16 times, and the inaction strategy was replicated8 times. For each simulation, the expected outcome iscalculated as the product of the mean outcome, and theprobabilities assigned to the hypotheses assumed for thatsimulation. For each strategy, the sum of its probabilityproducts adds to one, and the expected outcome iscalculated as the sum of the expected outcomes for eachcombination of hypotheses possible. Initially we assignedeach alternative hypothesis for our management strategiesequal probabilities.

Sensitivity Analysis. We conducted a sensitivity analysisusing the probabilities assigned to alternative hypothesesacross the full three-dimensional probability space forrate of patch spread, rate of long-distance dispersal events,and control effectiveness. This allowed us to identifystrategies that are robust to uncertainty in these compo-nents and to identify data gaps that are critical for ourability to predict which management strategies are the mosteffective.

Performance Measures. We examined two model outputsfrom each simulation that were relevant for our questions:the cumulative area treated in the invaded and establishedstates over a 50-yr period and the integral of the areainvaded over time in each state. Because the state of everypolygon was only printed every ten time-steps, the areacovered by crested wheatgrass over time was linearlyinterpolated. We assumed that the percent of a polygoncovered by crested wheatgrass was 30% in the invaded and90% in the established states.

Results and Discussion

The cumulative area covered by crested wheatgrass overthe 50-yr simulation period varied by a factor of nine, from6,141 ha for the large-patch–first strategy, with twice thecurrent budget under the hypotheses of effective control,slow spread, and few satellites, to 53,568 ha for theinaction strategy under the hypotheses of fast spread andmany satellites (Table 1). The cumulative area treated overthe 50-yr simulation period ranged from 0 ha under theinaction scenario to 2,675 ha for the large-patch strategy,with double the current budget under the fast-spread andmany-satellite hypotheses.

Differences in outcomes between the two managementstrategies were clear (Figure 3). While the early detectionand control scenario (Figure 3b) eliminates all small


patches and reduces the total number of patches, but leavesseveral very large patches on the landscape, the strategy thatprioritizes the largest patches (Figure 3c) reduces their size,but results in many more patches overall.

Parameter Sensitivity. The strategies that treat larger areasresult in less crested wheatgrass remaining after 50 yr in oursimulations (Figure 4). However, it takes fewer small-patch

treatments to achieve equivalent effectiveness to the large-patch treatment program. To understand the implicationsof uncertainty with respect to the probability assigned tothese hypotheses, we conducted a sensitivity analysis for thefull three-dimensional probability spaces for the inactionsimulations (Figure 5), and for the four simulations inwhich treatments were applied (Figure 6). In the absence ofany treatment, the average annual coverage of crestedwheatgrass in the park over a 50-yr period ranges from 920to 1,060 ha (Figure 5). Most of the variation in this rangeis explained by the probability assigned to the fast- vs. slow-patch spread hypothesis, whereas varying the probability oflong-distance dispersal events had very little effect oncrested wheatgrass cover after 50 yr.

Note that the many new patches setting sometimesresults in a lower cumulative area invaded over the courseof the simulation (Table 1). This is true in 33% (6 out of18) of all possible pair-wise cases where all other parametersare equal. The reason this occurs is because we are using astochastic simulation model based on probability distribu-tions, not a deterministic model. At each time-step, themodel draws from a Poisson distribution to determine thenumber of new patches from outside of the landscape thatwill be initiated in the study area. For the many new-patches hypothesis we used a higher number (2) as theaverage for the distribution vs. (1) for the few-patchhypothesis. However, given the stochastic nature of theprocess in some time-steps, there could be a large numberof new patches for the few-patch hypothesis or even zeropatches under the many-patch hypothesis. Additionally,there are other stochastic processes occurring during thesimulations, including control success rates and spread

Figure 3. Sample spatial outputs for a portion of the park knownas Larson Block in year fifty of three simulations. Crestedwheatgrass infestations are shown in black. Results shown are forthe most pessimistic assumptions (fast spread, many satellites,and low control effectiveness). Strategies shown are (A) inaction,(B) current capacity prioritizing early detection and control ofnew patches, and (C) current capacity prioritizing the control oflarge existing infestations. Long linear infestations occur alongroad rights-of-way.

Figure 4. Simulated outcomes of average crested wheatgrass areaand total treatments over 50 yr for Grasslands National Park,assuming equal probabilities for all alternative hypotheses ofspread rate, control effectiveness, and satellites. Strategies areinaction (No-MGT), prioritize large-patch edges (LPE), andprioritize the smallest patches (SP). Annual control budgets areeither 50 or 100 polygon ha/yr (124 to 248 ac/yr).


distances that could result in higher cumulative areainvaded for the few-patch hypothesis. For the majorityof the simulations (66%), the many-patch hypothesishas greater cumulative area invaded: and, on average, thereis 1.5% more area invaded with the many-patchhypothesis.

Our decision analysis demonstrated the interactionbetween control effectiveness and control strategy on theability to manage crested wheatgrass invasions in ourscenario landscape (Figure 6). When budgets are sufficientto treat 100 ha of invaded crested wheatgrass per year, theprobability that the large-patch or small-patch treatments isthe highest ranked strategy changes as a function of controleffectiveness. The highest ranking strategy shifts graduallyfrom the focus on small-patch control when controleffectiveness is low, to large-patch control when controleffectiveness is high (Figure 6). When budgets aresufficient to control only 50 ha of crested wheatgrass peryear, control effectiveness has no effect on rank, with small-patch focus always ranking better than the large-patchstrategy (Table 1).

The Role of Control Effectiveness in Control Strategy. Controleffectiveness has the most complex effects on the overallarea treated in a control program (Figure 6). Treatment of50 ha of small patches of crested wheatgrass per year ranksfirst for all values of control effectiveness below 100%.Between 80 and 100% effectiveness, annually treating50 ha of small patches slips to third in terms of cost behindsmall-patch and large-patch treatment of 100 ha/yr.Similarly, annual treatment of only large patches totalling50 ha annually declines from second to fourth rank,between 60 and 100% control effectiveness. The beststrategy for controlling crested wheatgrass while treatingthe smallest area is only sensitive to changes in controleffectiveness when that effectiveness is at or close to 100%.

Figure 5. Average crested wheatgrass coverage (ha) over 50 yrwith no management as a function of the probability assigned tothe 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 ofpanels) is displayed with respect to the probability assigned to the effective-control hypothesis (columns). Within each panel, theprobabilities assigned to the many-satellite hypothesis and the probability assigned to the fast-spread hypothesis are shown as inFigure 5. The probability of many satellites varies along the x-axis, while the probability for fast spread varies along the y-axis. Eachmajor column of panels represents a point in probability space for effective control. Probabilities for the complementary alternativehypotheses (ineffective control, few satellites, slow spread) are equal to one minus the probability shown in the figure. The strategy thatresulted in the least area covered by crested wheatgrass over time, or the least area treated, is labelled and shaded within the region ofparameter 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.


With a program that has both a large budget andeffective control, it is possible that control efforts will notbe overwhelmed by spread from large patches. Doublingthe current capacity for treatment can shift strategyrankings such that prioritizing large existing infestationsranks first, but only under conditions in which control ishighly effective or when spread is slow and the rate ofappearance of new infestations is high. This cannot besustained if the effectiveness of control effort is low.Wadsworth et al. (2000) showed that under conditions inwhich long-distance dispersal is the dominant form ofdispersal, it is better to prioritize larger patches. Our resultsare in agreement with this conclusion.

Our results suggest an interaction between controleffectiveness and patch size. The biology of crestedwheatgrass suggests that monitoring and control of smallpatches should be adopted as a priority by land managers,largely because of the relative infrequency of long-distancedispersal. While seed production of crested wheatgrass ishigh (Heidinga and Wilson 2002; Pyke 1990) most seedsdisperse short distances (Marlette and Anderson 1986).Indeed, what is more striking with crested wheatgrass is itstemporal pattern of dispersal. Seeds are released from theflowering culm over an extended period of time (Pyke1990) and can remain resident in the seedbank for 4 yr ormore (Wilson and Partel 2003). Hence, crested wheatgrasstends to form virtual monocultures in which there is astrong positive relationship between plant cover andseedling density (Marlette and Anderson 1986). Thismeans that attempts to control an established infestation ofcrested wheatgrass may be overwhelmed by its ability toreestablish within large infestations. While this does notmean that small infestations are easy to control, it suggeststhat control effectiveness may be inversely related to patchsize, with greater control efficiency on a strategy that targetssmaller patches.

Some studies have shown that increased short-termfunding can reduce the overall long-term expenditure offunds for controlling invasive weeds (Higgins et al. 2000b;Taylor and Hastings 2004). In our simulations, this is onlytrue under conditions in which control efforts are highlyeffective. Under these conditions, increased short-termcapacity can reduce levels of crested wheatgrass quicklyenough that the required level of effort subsequentlydecreases steadily over time. Otherwise, under conditionsof imperfect control, doubling of current capacity alwaysresults in greater expenditures over the 50-yr period. Landmanagers are therefore faced with a trade-off: do they trustthat long-term control is highly effective (Wilson andPartel 2003) and allocate more resources to crestedwheatgrass control, foregoing other long-term priorities,or do they maintain levels of treatment at current capacityand potentially tolerate greater levels of crested wheatgrasswithin the landscape over the long term? Research to both

measure and improve control effectiveness will help resolvethis impasse and may result in a clearer set of decisions.

The Role of Financial Constraints on Control Strategy. In ourmodel simulations, the trade-off between short- and long-term control was resolved in part by the financial realitiesof invasive species management. In the absence of a budgetsufficient to entirely control large crested wheatgrasspatches, the best strategy was always to focus resourceson small patches (Table 1). Regardless of how effectivecrested wheatgrass control may be, a budget that isinsufficient to control large patches constrains the managerto focus on small patches. This occurs because attempts tocontrol large patches without adequate resources to do socomprehensively are always overwhelmed by the capacity ofthe patches to spread. Under these conditions, allocatingresources to early detection and control of new infestationsalways ranks better, both in terms of total area treated over50 yr and in terms of the average area covered by crestedwheatgrass over this time period.

Our results show that under current levels of fundingand uncertainty, the strategy that most often ranks besttowards reducing the coverage of crested wheatgrass is oneof early detection and control of new infestations, as hasbeen recommended by Simberloff (2003). This result isconsistent with the conclusion drawn by Moody and Mack(1988): that ignoring nascent foci results in more largepatches in the future, and that focusing treatments on largepatches may be ineffective because spread from thesespatches tends to overwhelm control efforts.

While our simulations considered a base budget thatallows for 50 ha of restoration per year as outlined in therevegetation plan for Grasslands National Park, the actualbudget levels in recent years that are allocated to restorationare far lower, in the order of only 6 to 12 ha of CWGrestoration per year. If land managers wish to considerincreasing the capacity for treatment, there are some keyuncertainties that must be resolved to determine whethermanagement should prioritize early detection and controlof new infestations, or reducing the size of large existinginfestations. As already stated, if control efforts are highlyeffective and budgets are high then allocating resources tolarge existing infestations always ranks better thanprioritizing early detection and control of new infestations.Research into the effectiveness of control efforts has beenconducted at Grasslands National Park for over a decade(Ambrose and Wilson 2003; Bakker and Wilson 2004;Wilson and Partel 2003; Wilson et al. 2004), but always insmall plots (# 30 m2). This has guided the park’s currentmanagement actions (Sturch 2005), but understanding ofcontrol effectiveness in large-scale restorations (# 50 ha)over the long-term is still poor. Consideration of controleffectiveness appears to be restricted to invasive speciescontrol simulation models (Eiswerth and Johnson 2002;


Leung et al. 2002; Rinella and Sheley 2005; Shea andKelley 2004), and has not become a consideration that fieldstudies are commonly reporting, despite its importance fordecision making. If control efforts are not effective, thenother key uncertainties are the rates of patch spread andlong-distance dispersal. Rates of patch spread have beenmeasured in Grasslands National Park (Hansen 2006;Henderson 2005), but rates of long-distance dispersal havenot, owing in large part to the expense of establishing asampling protocol that has sufficient power to detect long-range dispersal events.

Our analysis first assumes that the ranges assigned toparameters for alternative hypotheses about spread andcontrol are representative of the full plausible range ofpossibility for these parameters, and secondly, thatdetection of new patches is relatively inexpensive. It isimportant to verify that the values of our parameters arewithin plausible ranges even if managers are not consid-ering an increase in current capacity. For example, theaverage number of new infestations in the park, modelledwith the Poisson distribution, was based on very littleavailable information. One possible approach to improvingthis would be to establish long-term sampling areas for newinfestations that are distant from any existing sources. Therate at which new infestations appear in these areas couldbe used to inform the long-distance–spread-parametersused for future simulations. Such a monitoring programwould have the additional benefit of detecting newinfestations early enough that the cost of treating themwould be low. If detecting new infestations is expensive andrequires a great deal of resources, it may be more effectiveto focus on patches that are already known. However, asnoted in our description of control costs, it is much moreexpensive to control large vs. small patches because of therequirement for seeding. Using real monitoring costs as aguide, an observation model that explicitly considers thetradeoffs between monitoring and treatments could bedeveloped. This also reinforces the need for practitioners toimprove their knowledge on control effectiveness withevery control program they implement.

Structured Decision Analysis. It is in managing the keyuncertainties and assumptions that the formal process ofdecision analysis plays a useful role. Decision analysis hastwo elements: a probability model that assigns probabilitiesto uncertain (biological) events, and a values model thatweighs the costs and benefits to all parties of the range ofpossible actions recommended by the probability model(Maguire 2004). Hence, decision analysis acts as more than apopulation model by incorporating a cost to stakeholders ofmanagement activities, affecting how priorities are set in acomplex management environment (Drechsler and Burg-man 2004; Ellison 1996). In our case, the values of the parkmanagers are well understood by all stakeholders, and

actions to control crested wheatgrass have predominantlyeconomic costs with few values conflicts. Nevertheless,crested wheatgrass continues to be seeded and cultivated asan important hay crop all around the park. Thus, it is clearthat if control efforts by land managers for crestedwheatgrass were to attempt to extend beyond the parkboundary, our ‘‘values’’ landscape would become consider-ably more complex and hence would alter decision making.

This model is a first approximation to our description ofthe problem. Subsequent to this analysis we have identifiedfour shortcomings and identified future analyses that wouldimprove the level of confidence in our results. First, thetransition between the initial and established states isartificial, and there is more likely a gradual continuumbetween a polygon with a single crested wheatgrass plantand one that has 100% cover of crested wheatgrass. Thecomplete transformation of the community is somewhatcompensated for by a minimum residence time of 10 to15 yr in the invaded state before transition to theestablished state was possible. A second shortcoming isthat it is difficult to relate control effectiveness parametersback to monitoring data on control effectiveness. Controleffectiveness parameters that are easier to quantify wouldmake it easier to relate to the percent reduction in crestedwheatgrass cover on a polygon. Third, our treatmentbudgets are simulated in terms of polygon area, rather thanthe absolute coverage of crested wheatgrass. Coverage ofcrested wheatgrass varies according to state, but this can notbe incorporated into our budget ceilings for treatments. Abetter approach would incorporate a percent coverrelationship per ha against time since invasion. Treatmentceilings would then be applied against total area covered bycrested wheatgrass rather than polygon areas. Reductions incover from different levels of control effectiveness wouldlead to setting back the age-cover relationship. Finally, wedo not explicitly consider costs and limitations onmonitoring efforts. This could be incorporated in a stateand transition formulation in which crested wheatgrass ispresent but unknown, or present and known, to managers.Monitoring efforts could be incorporated into the state-change rules that transition polygons from unknown toknown states, assuming different detection probabilities.

Our decision analysis approach to the management ofinvasive plants would be well suited to a broader adaptivemanagement framework (Shea et al. 2002) because itexplicitly deals with uncertainty and makes predictionsabout the performance of alternative management strategiesunder different hypotheses. As an example, managers couldsubdivide the affected landscape into different experimentalunits and use alternate strategies in each. Monitoring ofcrested wheatgrass population densities and locationswithin each unit would help determine if our predictionsregarding the most effective management strategies reallyare correct.


Measurements of parameters conducted within each unitwould enable us to improve our model and increase ourconfidence in future decisions. Based on these experimentalresults, both the parameter ranges chosen and theprobability space used for sensitivity analysis could berefined. Accurate information on control effectiveness was akey uncertainty in our model, and this can best beimproved in a managed setting using adaptive managementapproaches.

There are various situations under which adaptivemanagement may not be possible, including lack ofresources, long response times, difficulty monitoring, andothers (Shea et al. 2002). Indeed, there can be more tocharacterizing consequences and analyzing cost-benefit–trade-offs than the suite of variables we have used. In thiscase, decision analysis will not reduce uncertainty, but canat least identify the most effective strategies to pursue untilmore information or resources become available. This wasthe case with crested wheatgrass, where we found thatunder current budget levels and the parameter ranges weidentified, a strategy of directing control efforts at detectingand treating new patches is always better than focusing onlarge known infestations.

Sources of Materials1 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 atRisk Recovery and Education Fund, Grasslands National Parkof Canada, and ESSA Technologies Ltd. We thank RussWalton for thoughtful comments on the initial model design.Kelly Robson provided assistance in the preparation of thefigures. Two anonymous reviewers, Donald Robinson, DarcyHenderson, and Judy Toews reviewed an earlier version of themanuscript.

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Received February 16, 2009, and approved July 28, 2009.


frid and wilmshurst 2009

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