Abstract

This report examined how decisions to invest in invasive species management on public lands could incorporate

economic concepts to better gauge the level of social benefits generated and how optimization models could be

applied to produce the maximum potential gains in ecosystem services. Findings suggested that management decisions were effectively modeled using GIS-based decision support tools, providing a means to reveal assumptions

and allow greater input by the public and scientific community into the decision-making process. The optimization

model results suggested that benefits achieved through invasive species treatment might be improved if multiple

ecosystem service benefits were considered simultaneously when choosing sites and treatment options rather than

choosing options that maximized a particular ecosystem service.

Prioritizing Invasive Species

Management by Optimizing

Production of Ecosystem

Service Benefits

Contractor and Cooperator Report No. 44

July 2008

By Lisa A. Wainger, Dennis M. King, Richard N. Mack, Elizabeth W. Price,

and Thomas Maslin

This study was conducted under a cooperative research contract with

USDA’s Economic Research Service (ERS) Program of Research on the

Economics of Invasive Species Management (PREISM): contract number

43-3AEM-3-80092 (ERS project representative: Craig Osteen). The views

expressed are those of the authors and not necessarily those of ERS or

USDA.
Prioritizing Invasive Species Management 

by Optimizing Production of Ecosystem Service Benefits 

Final Report to USDA ERS PREISM Program 

ERS Project Manager: Craig Osteen, USDA, Economic Research Service 

Resource Economics Division 

Agreement #: 43-3AEM-3-80092 

August 31, 2007 

Lisa A. Wainger1, Dennis M. King1, Richard N. Mack2, Elizabeth W. Price1 and Thomas Maslin3

1

University of Maryland Center for Environmental Science, Solomons, Maryland 

2

Washington State University, Pullman, WA 

3

Duke University, Durham, NC (formerly of UMCES) 
ii

Acknowledgements 

The authors gratefully acknowledge the cooperation of the BLM offices in 

Washington, D.C., Twin Falls, Idaho and Boise, Idaho and wish to specifically thank the 

following people from BLM for their substantial contributions: 

– Mike Pellant 

– Brandon Brown 

– Tom Roberts 

– Jack Hamby 

– Tom Miles 

– Scott Lambert 

– Scott Uhrig 

– Joe Russell 

– Jesse German 

– Cindy Lou McDonald 

We received generous help in the form of data, advice and other input from: 

• Dave Pyke, Michael Kochert, USGS 

• Bruce Ackerman and Regan Berkley, Idaho Department of Fish and Game 

• Gina Wilson, University of Idaho, Landscape Dynamics Lab 

• Chris Clay, Idaho Department of Lands 

• Gary McCuin, Nevada Department of Agriculture 

• John McLean, Resource Concepts, Carson City, Nevada 

• Jim Opaluch, University of Rhode Island 

• Kitty Smith and Craig Osteen USDA 

• Jillian Rayburn, Nicole Chigounis and Abby Lund, University of Maryland 

Center for Environmental Science 

In addition to those previously acknowledged, we would like to thank the 

following people for their participation in the Cheatgrass Management Workshop and for 

providing valuable input into our project: 

• Bureau of Land Management 

o Bill Dragt 

o John V. Martin 

o Sharon Paris 

o Sheldon Wimmer 

• USFWS 

o Bill Leenhouts 

• USDA Forest Service 

o Nancy Shaw 

o Lynn Kinter 

• USGS 

o Cindy Salo 

Finally, we want to thank the Program of Research on the Economics of Invasive 

Species Management (PREISM), Economic Research Service, U.S. Department of 

Agriculture for providing funding and the many others, including the reviewers of this 

report, who generously shared their expertise with us. 

Cover Figure: Top image shows an Idaho landscape dominated by native vegetation and lower 

figure shows an Idaho landscape dominated by invasive annual grasses of cheatgrass (Bromus 

tectorum) and medusahead (Taeniatherum caputmedusae ssp. asperum). Pictured in photo from 

left to right are David Pyke (USGS), Mike Pellant (BLM, Coordinator Great Basin Restoration 

Initiative), Susan Gianettino (BLM - Idaho Deputy State Director for Resources). 
iii

Table of Contents 

Acknowledgements...................................................................................................... ii 

Executive Summary........................................................................................................ vii

1. Introduction................................................................................................................ 1

1.1 Analytical Framework ......................................................................................... 2 

1.2 Research Approach .............................................................................................. 3 

1.3 Why this approach?.............................................................................................. 5 

1.4 Case Study ........................................................................................................... 6 

2. Problem Formulation .............................................................................................. 22

2.1 Optimization Model Overview .......................................................................... 23 

2.2 Short vs. Long-Term Benefits Analysis............................................................. 24 

3. Benefits Assessment................................................................................................. 25

3.1 General Benefits Model ..................................................................................... 25 

3.2 Change in Benefits with Treatment ................................................................... 26 

3.3 Measuring bmax - Maximum Potential Benefits of a Site................................... 34 

3.4 Metrics Used to Measure bmax for all Services .................................................. 39 

3.5 Benefit Measurement Discussion ...................................................................... 55 

4. Evaluation of Treatment Costs............................................................................... 55

4.1 Facility Location – Application of Location Theory ......................................... 55 

4.2 Cost Model Framework ..................................................................................... 56 

4.3 Cost Model Discussion ...................................................................................... 68 

5. Restorability ............................................................................................................. 70

5.1 Introduction........................................................................................................ 70 

5.2 Measuring Recoverability and Restorability ..................................................... 72 

5.3 Literature Review of Restorability Data............................................................ 73 

5.4 Using Elicited Best Professional Judgment to Score Restorability ................... 75 

5.5 Statistical Evaluation of Restorability Data....................................................... 77 

5.6 Restorability Model Discussion......................................................................... 84 

6. Optimization Modeling to Select Treatment Sites and Treatment Intensities... 85

6.1 Optimization Model Background ...................................................................... 85 

6.2 Optimization Model Implementation................................................................. 89 

6.3 Optimization Model Results and Discussion..................................................... 91 

7. Conclusions............................................................................................................. 106

7.1 Management Implications................................................................................ 106 

7.2 Recommendations for Further Study............................................................... 110 

8. References............................................................................................................... 111

Appendix A. Historical Progression of Cheatgrass Invasion................................... A-1

Appendix B. Interview Protocol Developed to Evaluate Restorability Factors..... B-1
iv

List of Tables 

Table 1. Potential Welfare Impacts of Cheatgrass ......................................................... 21 

Table 2. Ecosystem Services Used in Benefits Analysis ............................................... 22 

Table 3. Indicators Identified to Assess Relative Economic Benefits of Four Ecosystem 

Services ............................................................................................................ 40 

Table 4. Site Quality Factors Used when Combining Service Benefit Indicators ......... 53 

Table 5. Benefit Indicator Scores for Selected Sites...................................................... 54 

Table 6. Variables Developed Using GIS Data and Analysis to Test Effects on 

Treatment Costs ............................................................................................... 59 

Table 7. Variables Considered for Empirical Cost Model............................................. 64 

Table 8. Coefficient Estimates from OLS Model .......................................................... 65 

Table 9. Journey Costs per Hour and per Trip ............................................................... 69 

Table 10. Restorability Factors Rated by Restoration Practitioners ................................ 77 

Table 11. Variables Used in Restorability Statistical Model ........................................... 79 

Table 12. Parameter Estimates for Ordinal Logit Model of Restoration Success............ 80 

Table 13. Summary of Restorability Model Results........................................................ 80 

Table 14. Probability of Treatment Success by Treatment Intensity Given Percent 

Cheatgrass Cover Pre-Fire ............................................................................... 83 

Table 15. Illustration of Strings and Related Value Measures for Cheatgrass 

Optimization..................................................................................................... 87 

Table 16. Comparison of Solution Sets without and with Limit on Number of Sites 

Treated ............................................................................................................. 92 

Table 17. Optimization Solution Sets Summary for Different Ecosystem Service 

Weightings ....................................................................................................... 96 

Table 18. Distribution of Benefits among Ecosystem Services when Service Weights 

Varied............................................................................................................... 97 
v

List of Figures 

Figure 1. Site Map of BLM Twin Falls District in Southern Idaho ................................ 14 

Figure 2. Treated and Untreated Fires 2001-2003........................................................... 23

Figure 3. Benefits Equation Showing Responsiveness of Benefits to Parameter m and 

Percent Native Cover ....................................................................................... 28 

Figure 4a. Defining patches used in spatial pattern metrics.............................................. 32 

Figure 4b. Effect of Fire on Landscape Connectivity ....................................................... 32 

Figure 5. Change in Largest Patch Index (LPI) with Fire Size for 46 Burned Areas in 

Idaho and Nevada............................................................................................. 33 

Figure 6. Habitat Quality for Sage-Grouse...................................................................... 41

Figure 7. Map of Forage Production Quality Indicator: Animal Unit Months per 

Hectare ............................................................................................................. 43 

Figure 8a. Potential Trip Density ...................................................................................... 47 

Figure 8b. Habitat Quality over Trip Density Zones......................................................... 47 

Figure 8c. Substitutable Sites ............................................................................................ 47 

Figure 8d. Lowest-Risk - Highest Benefit Sites................................................................ 47 

Figure 9. Area Accessible within 1.5 Hours Travel Time of Burned Area..................... 49 

Figure 10. Impedence Map Representing Travel Time per Landscape Grid Cell............. 61 

Figure 11. Cumulative Journey Time Map........................................................................ 62 

Figure 12. Natural Log of Cost per Acre vs. Natural Log of Fire Size ............................. 66 

Figure 13. Influence Diagram of Restorability.................................................................. 71 

Figure 14. Reversibility of System Decline ...................................................................... 72 

Figure 15. Seed Type (Native vs. Non-Native) and Project Success (2001-2003) ........... 81 

Figure 16. Hypothesized Relationships between % Cheatgrass Cover Pre-Fire and 

Natural Recovery or Restorability with Maximum Treatment Intensity ......... 82 

Figure 17. Optimization Model Solution with No Limit on Treated Fires, 

Equal Weight on All Benefit Categories) ........................................................ 93 

Figure 18. Agency Choices vs. Optimization Results with 10-Site Limit, 

Equal Weight on All Benefits)......................................................................... 93 

Figure 19. Cost-Effectiveness vs. Fire Size....................................................................... 94 

Figure 20. Typical Distribution of Benefits among Service Categories in Optimization 

Model Results .................................................................................................. 97 

Figure 21 a-d. Maps of Solution Sets from Optimization Model and Agency Choices 

in 2002............................................................................................................ 101 

Figure 22. Risk-Weighted Benefits vs. Costs of Model and Agency Selected Options.. 103 

Figure 23. Comparison of Per Acre Benefits for Options Selected by Optimization 

Model and Agency ......................................................................................... 104 
vi

Prioritizing Invasive Species Management by Optimizing 

Production of Ecosystem Service Benefits 

Lisa A. Wainger, Dennis M. King, Richard N. Mack, Elizabeth W. Price, and 

Thomas Maslin 

Contractor and Cooperator Report No. 44 

Abstract 

This report examined how decisions to invest in invasive species management on public 

lands could incorporate economic concepts to better gauge the level of social benefits 

generated and how optimization models could be applied to produce the maximum 

potential gains in ecosystem services. Findings suggested that management decisions 

were effectively modeled using GIS-based decision support tools, providing a means to 

reveal assumptions and allow greater input by the public and scientific community into 

the decision-making process. The optimization model results suggested that benefits 

achieved through invasive species treatment might be improved if multiple ecosystem 

service benefits were considered simultaneously when choosing sites and treatment 

options rather than choosing options that maximized a particular ecosystem service. 
vii

Executive Summary 

Goals 

Federal agencies that manage land in the Intermountain West, such as the U.S. 

Department of Agriculture’s Forest Service and Bureau of Land Management, are 

concerned about finding a cost-effective way to preserve a range of social benefits 

generated by public lands, including those associated with food production, recreational 

opportunities, aesthetic enhancements, and existence values for species or natural 

systems. A potential threat to maintaining these ecosystem services is invasive species 

that can dramatically alter essential ecosystem function and put human health and welfare 

at risk. To manage risks, the managers of these lands devote funds to invasive species 

control. Since treatment funds are limited, managers must choose from many potential 

restoration sites and treatment intensities. Their goal in most situations is to choose 

combinations of treatment options that maximize social benefits based on available 

funding, labor, and equipment. 

The goals of this project were to: 

1. Demonstrate how economic principles could be incorporated into a decision 

support framework, usable by natural resource managers, to assess and compare 

the social benefits and cost-effectiveness of invasive species treatment 

alternatives 

2. Evaluate effect on treatment decisions of explicitly accounting for spatial 

heterogeneity of costs, benefits, and risks 
viii

3. Evaluate whether promoting particular ecosystem services over others would 

change cost-effectiveness of site-treatment options 

4. Evaluate whether existing data and information were adequate to create practical 

quantitative decision support tools 

5. Assess the potential usefulness to managers of modern quantitative optimization 

techniques for choosing treatment options. 

The aim was to demonstrate that decisions about where to invest in invasive species 

management could be based on concepts and applications of location and investment 

theory common to other types of management and investment decisions. 

Major Findings 

1. Decision-support tools that incorporate economic principles and reveal underlying 

assumptions and value judgments provide a basis for both expert and stakeholder 

involvement in decision-making and promote cost- and risk-conscious solutions 

2. Available data and knowledge were sufficient to capture the decision process in a 

standardized framework that could be used to develop consistent decision criteria. 

3. The optimization model results suggested that managers could increase benefits of 

treatment by selecting sites that maximized multiple service benefits 

simultaneously, rather than the apparent current practice of selecting sites that 

maximized only one service benefit. 
ix

Case Study 

Researchers relied on a case study of one of the best studied invasive species in North 

America, cheatgrass (Bromus tectorum). After reviewing much of the available 

information about this species, models were developed to: measure relative benefit 

indicators of 4 ecosystem services by location; estimate treatment costs by location; and 

estimate restorability of ecosystem services by location. Site-specific measures of costs, 

benefits, and restorability were then combined within an optimization framework to 

generate optimal sets of treatment options that maximized a weighted sum of social 

benefit indicators subject to a fixed budget constraint. The ecosystem services selected 

for final evaluation were 

1. Support of recreational antelope hunting; 

2. Forage production for cattle; 

3. Property protection from fire; and 

4. Existence values associated with sage grouse. 

The sensitivity of the optimal solution to different weights assigned to these four benefit 

measures was also tested. 

The analytical framework and optimization model were developed by working closely 

with Federal land managers in the region to specify a framework that addressed local 

decision support needs. Local and regional technical expertise was elicited to build the 

underlying models of the decision framework using the best available research and data. 

However, it became apparent, that even for cheatgrass, one of the most-studied invasives 

in the United States, a great deal of quantitative information was lacking. As a result, the 
x

model relied more heavily than planned on the professional judgment of managers, 

scientists, and the research team. This situation should be expected for other invasives 

where the characteristics of the invasive species and its effects on ecosystem services are 

even less well understood. 

This work built on a more general decision framework that had been previously 

developed by the authors. In this implementation, the availability of data and technical 

understanding of the cheatgrass problem were evaluated for their adequacy to support an 

optimization model aimed at selecting management options to maximize social benefits 

under budget and other constraints. Each management option consisted of a choice of 

treatment site and treatment intensity when applying a preventative treatment regime 

following fire. 

A Spatially Explicit Approach to Evaluating Cost-Effectiveness 

To capture the most important differences among treatment locations, both cost and riskadjusted benefits were assessed and compared using as much location-specific 

information as possible. Site conditions and characteristics of the landscape surrounding 

treatment sites were incorporated to differentiate between the levels and qualities of 

ecosystem services protected or restored at sites, estimate likely treatment costs, and 

evaluate the likelihood that treatment would improve such benefits. Benefits were 

adjusted for treatment performance risk by reducing benefit indicators in proportion to 

the probability of successful outcomes of preventative treatment. 
xi

The approach, grounded in location theory, made use of available GIS data and analysis 

techniques to consider the effect of location on all aspects of cost-effectiveness, which 

formed the basis of site selection within the optimization model. For example, the 

research evaluated the effect of travel time on treatment costs, the effect of location on 

the number of potential recreational users, and how land cover configuration affected 

habitat quality. In addition, site and landscape factors that contributed to the expected 

recoverability and restorability of sites were used to generate risk-adjusted expected 

benefits of treatment. Such calculations would not have been possible without a spatially 

detailed approach. 

As expected, many empirical obstacles were found in the development of statistically 

determined quantitative production functions that could link site characteristics to 

realized social benefits or site response to treatment with outcomes. Even the basic 

aspects of risk created by the invasive species were unquantifiable and of questionable 

certainty. Only cost accounting was based on statistical analysis of treatment spending. 

Best professional judgment was used to characterize restorability of sites (with treatment) 

and recoverability (without treatment), although interviews were supplemented by 

statistical analysis of an available database on restoration outcomes. 

In lieu of quantitative relationships between invasive species and benefits, previous 

benefit evaluation framework and applied indicators of relative ecosystem service 

benefits were built upon to distinguish treatment sites and treatment intensities. First 

principles of ecology and economics, and best professional judgment, were used to link 
xii

characteristics of the built and natural environment to ecosystem service quality. 

Economic literature and conceptual models were used, where applicable, to identify 

indicators of relative service value. 

A parsimonious set of benefit indicators was selected to reflect aspects of relative value 

of ecosystem services produced at a site, including: 

Ecological site qualities 

Location attributes contributing to site quality 

Cost of access 

Presence of complementary goods 

Scarcity and substitutability of ecosystem service benefits 

Risk of service disruptions 

An example for recreational hunting benefits (antelope hunting) was used to demonstrate 

how indicators were derived using conceptual models developed from models and 

understanding available in the economic literature. 

Optimization Model 

The results of the benefits, costs, and restorability modeling formed the basis of an 

optimization model developed using commercially available optimization software. The 

use and demonstration of such software was intended to facilitate increased use of such 

tools by resource management agencies. Although optimization models are often 

criticized for failing to capture important aspects of management decisions, a model was 

developed with an intermediate level of detail to screen many sites. Limitations due to 
xiii

data quality and the ability to demonstrate and quantify possible harm from invasive 

species were of greater concern than limitations of the optimization framework. 

The optimization model was constructed from a social planner perspective, as it sought to 

maximize net social benefits through the choice of treatment sites and intensities. The 

budget constraint and weights applied to different ecosystem service benefits were 

adjustable to reflect alternative sets of potential management goals. Availability of spatial 

and non-spatial data was assessed for building such a system and it was apparent that a 

great deal of applicable data were available. However, the screening system would have 

been improved with the inclusion of additional regional data sets. In particular, a regional 

assessment of invasive species that included percent cover would have been valuable for 

assessing restorability and developing a regional treatment strategy. 

Results 

Despite the many concerns and caveats raised regarding the difficulty of developing the 

framework, the screening method, based on the best regional data and information 

available, was able to replicate choices made by managers who had detailed site-based 

information. This result suggests that available data are sufficient to capture the 

decision-making process in a standardized framework that could be used to develop 

consistent decision-making criteria. The value of a framework that replicates current 

decisions is that the process of site selection can be opened up to greater public and 

scientific input, rather than relying only on the negotiated solutions currently developed 

with limited public input. Since the framework could not be based completely on 
xiv

objective information, it seems particularly important that the approach developed here 

reveal the underlying assumptions, values, and tradeoffs associated with agency 

decisions; and enable researchers and stakeholders to understand how their input could be 

used. 

Although able to replicate the choices made by the agency, the optimization model 

generated greater increases in benefit indicators by selecting different management 

options, suggesting room for improvement in agency decisions. When benefit categories 

(ecosystem services) were all given equal weight, the optimization model solution set had 

only one selected treatment site in common with the agency’s choice set. When 

individual benefits were sequentially given full weight in the model and compared, to 

agency selections, all but one site was common to both sets. This indicated that agency 

managers picked sites to treat by choosing those that maximized change in benefits of a 

particular service (e.g., the best habitat site, the best fire prevention site) rather than 

choosing sites that jointly produced the highest net benefits from multiple services. 

Because the agency selected a different set of sites than the optimization model when all 

benefits were weighted equally (their stated goal), the model suggests that the overall 

level of benefits might be improved by choosing sites based on their production of 

multiple benefits simultaneously rather than as superlative producers of individual 

services. 

The optimization results are somewhat unusual in that they did not suggest tradeoffs 

needed to be made among services, but rather that services were complementary. 
xv

Optimization of one service benefit tended to bring along all other benefits 

simultaneously, if sites were treated as joint producers of multiple services. High benefits 

co-occurred for some, but not all, site-treatment options, demonstrating the value of the 

optimization model in identifying sites where treatment resulted in multiple service 

enhancements. It should be noted, however, that the optimization model result was 

dependent on the assumption that native vegetation would be established during 

restoration, a simplification of real-world outcomes. If differential establishment of 

seeded native versus seeded non-native plants were modeled, it would have created 

conflicts among the services provided at some treatment sites. Data were not available to 

measure or model the details of treatment outcomes. 

The optimization model constraint on the number of sites treated demonstrated the effect 

of resource limitations on the ability of managers to respond optimally to invasive 

species. The optimization model included the constraint of a maximum of 10 sites treated 

in order to match real-world constraints of managers with limited resources to allocate 

among sites. Model results were strongly affected by this constraint. When this constraint 

was removed, the optimization model solution included many small sites treated 

predominantly at low intensity, whereas the solution with the constraint of only 10 sites 

treated larger fires at low to high intensity. That smaller fires were selected by the 

optimization model when the number of sites was unconstrained, has important 

implications, as it indicates agencies might create more cost-effective treatment strategies 

by treating many small sites instead of a few large sites. Because this result is sensitive to 
xvi

many model assumptions, and because the optimization model does not necessarily find 

the globally optimal solution, further work is needed to confirm this result. 

The framework appears to succeed in representing most of the factors that managers 

consider when setting restoration priorities. In this way, the framework could be used to 

focus public debate over how public lands are managed and enable agencies to accept 

input from the public and scientific community. Agencies struggling with such decisions 

may find these experiences helpful in forming their choice to use optimization modeling 

for decision-making. In addition, managers may recognize that the many data gaps 

identified might be filled through alternative recordkeeping methods and treatment 

protocols. 

Overview of Cheatgrass Decision Support Model 

Objective: Maximize the weighted sum of standardized benefit indicators for four 

ecosystem services: 

Recreational hunting (antelope) 

Forage production 

Existence values for Sage-grouse 

Property protection from fire 

Constraints: Limits on spending and number of treated sites. 

Control Variables: Allocate 5 different levels of treatment among 68 potential 

treatment sites. 

Results: Optimal selection of treatment sites and treatment intensities that generate 

highest relative benefits and meet all constraints. The expected benefits, 

costs and risks of treatment differ from site to site based on specific sets of 

site characteristics and landscape context. 
1 

1. Introduction 

Increasingly, agricultural lands are being managed to provide a range of 

ecosystem services in addition to the production of food and other commodities (e.g., 

USDA Sustainability Programs). In the case of publicly-owned lands, decisions about 

how to make tradeoffs among different types of benefits through alternate management 

strategies are particularly challenging due to the multi-stakeholder nature of the 

management problem. Federal agencies are under pressure from a wide array of 

stakeholders to maximize production of ecosystem services such as rare species habitat, 

hunting opportunities, and agricultural productivity. As a result, they must either 

implicitly or explicitly weigh the different types of social and private benefits to be 

achieved through various types of land management. The choice of land management 

actions can depend in critical ways on the weight applied to different benefits and on the 

ability of alternative management actions to achieve management goals. The efficiency 

of such decisions can depend on the tools used to target management actions (Babcock et 

al. 1997). 

Invasive species are one of many forces changing landscapes and natural systems 

today and their influence on public lands in the U.S. spans at least the last 150 years 

(Mack 2003). Following a definition provided by Mack (2000), invasive species are 

defined as “species that establish a new range in which they proliferate, spread and 

persist to the detriment of the environment” and human welfare. Although non-native 

can refer simply to a species native to one part of the U.S. that has been carried to another 

part of the country where it has proliferated, these cases are less common. In the main, 

an invasive species in the U.S. refers to a species transported from outside the U.S. (most 

commonly from another continent) that has proliferated in its comparatively new nonnative range in the U.S. The key here is the recognition that the transport or dispersal of 

almost all current invasive species to and within the U.S. has been driven and facilitated 

by human activity. Thus, there is an inextricable link between the character, number, 

areal extent and influence of invasive species and a diverse array of human activities 

(Ruiz and Carleton 2003). 

Based on the growth in the diversity and extent of invasive species in the U.S. for 

the last 250 years (Mack 1991; 2003), there is every reason to anticipate this trend will 

not only continue but accelerate – a function of the increase in international commerce 

and human conversion of land to developed uses. This phenomenon is not unique to the 

U.S. – all parts of the planet and all ecosystems are susceptible to the establishment of 

invasive species, although to varying extents (Mack et al. 2000). Consequently, invasive 

species collectively should be legitimately viewed as one form of global change. 

Changes in the earth’s climate can and probably already have altered the trajectories for 

some biological invasions because the distributions of organisms are directly affected by 

climate (Dukes and Mooney 1999). Thus, the invasions on public lands will likely be 

influenced in the next 50 years and onward by climate change. Paradoxically, invasive 

species can also affect the rate of change in the earth’s atmosphere, as large regional 
2 

changes in the form of plant cover on the planet change the rate of CO2 sequestration 

(Mack et al. 2000 and references therein). 

Based on observations over at least the last 150 years, we know that most 

recognized invasions have been irreversible. Even where the distribution of an invasion 

has contracted, it has rarely led to the re-emergence of native species, but more 

commonly, results in the invasive being supplanted by another invasive species (Mack 

2000). These range contractions for invasive species have not been predicted and in 

some cases are difficult to explain, signaling that our predictive power could well 

diminish as climate change contributes to the multi-faceted aspects of uncertainty with 

respect to the range, intensity, and impacts of invasive species. 

Many invasions by plants, insects and animals threaten agricultural productivity 

and other ecosystem services. While lost agricultural revenues are relatively easy to 

tally, the values associated with the loss of habitat, loss of resilience of agro-ecosystems 

to pests and disease, changes in water cycles, and other effects are harder to capture. 

Although damages from invasives can be ameliorated on working landscapes, usually 

only with recurring effort and cost, the losses generally cannot be checked, much less 

reversed, on the vast public lands in the western U.S. As a result, the diversity of 

ecosystem services provided by these vast holdings held in the public trust is being 

depleted in a seemingly irreversible manner. 

Decisions about where to spend scarce management dollars on invasive species 

depend on a variety of factors but perhaps, most importantly, on the perspective and goals 

of the decision maker(s). Agency personnel respond to agency mandates, but may not 

have clear guidance for interpreting rules or setting priorities. By using a relatively 

formal decision-making framework that allows competing goals to be specified and 

weighted and that deals explicitly with tradeoffs and uncertainty, managers can better 

examine, explain, and justify the basis of their decisions. 

1.1 Analytical Framework 

With this project, we aimed to develop and test an analytical framework for 

prioritizing where to restore agro-ecosystems to maximize expected streams of ecosystem 

service benefits. In previous work, we established the basic framework of specifying a 

benefit accounting system that is based on 1) a wide range of potential social welfare 

impacts, 2) the probability of successfully restoring services that contribute to those 

social welfare impacts and 3) the costs of treatment. Here, we developed a case study, 

with the help of federal management partners, to test whether data and understanding 

were sufficient to rigorously evaluate and compare costs and risk-adjusted benefits of 

alternative management actions using this basic framework. 

This case study implementation was designed to evaluate whether data and 

understanding were sufficient to demonstrate links between ecosystem service benefits 

and invasive spread and whether that information could be used to guide management 

choices on restoration to the most cost-effective options. Further, we wanted to 
3 

demonstrate, using economic location theory concepts, how location, or landscape 

context, influences the relative value of ecosystem services and how the spatial 

heterogeneities of expected service values resulting from treatment might influence 

management decisions. In other words, we expected to demonstrate that decisions about 

where to invest in invasive species management could be informed by using concepts and 

applications of location theory and investment theory that are common to other types of 

management and investment decisions. 

This report is organized around five main themes: 

1. Background on the research approach and case study, including: 

a. Previous work on the cost-effectiveness framework 

b. History and ecology of cheatgrass invasion in the Intermountain West 

c. Management of cheatgrass in the Intermountain West 

2. Rationale for and organization of revised analysis framework 

3. Development of the benefit assessment module (idealized and practical) 

4. Development of a treatment cost model 

5. Development of a restorability model 

6. Evaluation of options within an optimization model 

1.2 Research Approach 

Two commonly used tools for evaluating and comparing effectiveness of 

proposed activities are cost-benefit analysis and cost-effectiveness analysis. In costbenefit analysis, all benefits are measured in terms of the monetary value of benefits to 

those affected. In cost-effectiveness analysis, both monetary and non-monetary measures 

may be used, usually to incorporate benefits that cannot be monetized, or to substitute 

non-dollar metrics for controversial monetary results. Cost-benefit analysis has the 

advantage that all benefits are measured in a common unit (dollars) that can be compared 

to costs to evaluate net social benefits of taking the action. Cost-effectiveness analysis is 

more commonly used to evaluate how to efficiently allocate funds that have already been 

dedicated and cannot be used to explicitly demonstrate net social benefits. 

We initially chose a cost-effectiveness framework to assess and compare alternate 

management options because of its advantages in terms of being able to incorporate a 

wide range of management concerns and goals. We used non-monetary measures to 

indicate changes in relative benefits among management options and compared those 

changes to costs in order to evaluate change in benefit indicators per dollar spent. We 

accounted for performance risk by incorporating whether treatment outcomes matched 

management goals. Changes in benefit indicators were therefore weighed by the 

probability that treatment would succeed in restoring ecosystem services to generate riskadjusted benefit indicators. 

To provide more flexibility in evaluating which combination of cost-effective 

options generated the highest level of benefits, we input the costs and risk-adjusted 

benefit measures into an optimization model. Cost-effectiveness analysis can generate 

many similarly cost-effective options, so the optimization model allows us to combine 
4 

options in many different combinations to arrive at a set that maximizes benefits for 

budget and logistical constraints. The optimization model still uses cost-effectiveness to 

judge options but allows us to allocate the budget most efficiently. 

The indicators of benefits were constructed to represent changes in the supply and 

demand of ecosystem services that flowed from treating a site. Treatment involved 

preventing domination of the vegetation by a non-native invasive species through postfire rehabilitation. The indicators were carefully selected to measure the quantity and 

quality of benefits that people would derive from site restoration. They did not represent 

willingness-to-pay or willingness-to-accept, but they did represent preferences and were 

intended to provide a practical means to capture relative social benefits. 

We recognized that we could not represent all the details of the important 

ecological and economic linkages that could affect the selection of an optimal treatment 

plan and still have a workable framework. Therefore, we sought an intermediate level of 

detail that would further the goal of developing an economically-based decision support 

system that was simple enough to be used, but that did not ignore the most important 

aspects of ecological complexity. 

The benefit assessment within both the cost-effectiveness framework and the 

optimization model were built upon a multi-criteria analysis of stakeholder objectives. 

The multi-criteria framework, in which different goals are represented and assigned 

weights, closely matched the decision-making techniques used by some of the regional 

resource management offices, even though managers did not arrive at their decisions 

through formal analysis. Our partners for this case study used a typical approach to 

decision-making whereby priorities for restoration were chosen through a negotiated 

process among a group of individuals, each of whom represented a particular interest 

such as hunting, ranching or an environmental concern. This approach matched our 

multi-criteria analysis framework which allowed users to assign weights to different 

benefit-generating ecosystem services that supported: hunting, ranching, property 

protection, and habitat (existence values). 

The steps we used to develop the decision support framework for resource 

managers can be summarized as: 

1. Characterize management problems and response options 

2. Identify ecosystem services affected by problem and frame benefits analysis 

3. Evaluate data available to inform quantification of benefits, costs & risks 

4. Develop risk-adjusted cost-effectiveness framework for decision support 

5. Test an integrated optimization approach for comparing options, including 

constraints and assessing uncertainty. 

Our previous work developing the structure of the framework resulted in conceptual 

models for assessing benefits and costs and a detailed indicator system for measuring 

relative benefits of ecosystem services (Wainger and King 2002, Wainger et al. 2001). 

This project continued that work by fleshing out the specific restorability model that 

could be used to assess risk-adjusted benefits, developing more detailed methods to 
5 

capture the change in social benefits due to a management action, and evaluating 

location-specific costs rather than relying on average costs of treatment per acre. 

Because location matters when assessing supply of and demand for ecosystem 

services, our methods characterized many aspects of the spatial arrangement of resources 

to capture the effects of service quality, or quantity on value. The benefits assessment 

considered site-specific qualities within the site and within the surrounding landscape. 

We included aspects of location that typically drive supply or demand of services such as 

proximity of users, scarcity or substitutability of services, and risks of disruptions to 

service flows. Not all aspects identified as important could be included in the final 

framework due to constraints on data availability or lack of mechanistic understanding. 

However, a great deal of spatial and supporting data sets were available to evaluate costs, 

risks and benefits and we applied novel analyses using a Geographic Information System 

(GIS) to quantify site and landscape characteristics that reflected expected changes in 

streams of future benefits with and without treatment. 

1.3 Why this approach? 

In making prioritization decision, managers must typically compare many sitetreatment intensity options and do not necessarily have the ability or the resources to 

monetize the many benefits derived from those treatments for each option. With this case 

study, we were testing whether it was possible to develop a system that managers could 

use to incorporate economic concepts into decision-making without introducing 

unsupportable cost or benefit estimates. The result was the development of a site 

screening tool that, by necessity, simplified economic and ecological complexity in order 

to create a manageable analysis tool. 

Throughout this report we will refer to the characteristics measured by the 

indicators as “benefits.” Although the indicators do not and cannot represent an explicit 

demonstration of net social benefits, they describe characteristics that we know (or 

hypothesize) contribute to social benefits. The reader is hereby cautioned that we have 

not demonstrated benefits from treatment but rather these indicators provide a practical 

proxy for comparing elements of value among management options. We take this 

approach with the understanding that complete technical and social preference 

information is not available for conducting more traditional types of benefit assessments. 

Despite the simplifications, our system more explicitly accounted for costs, risks 

and relative benefits than many types of economic decision-support methods, and as a 

result has the potential to be more revealing of assumptions and subjective judgments 

than less detailed models. Our management partners encouraged and cooperated with 

this approach out of their desire to enhance the quality of decisions and to create a more 

transparent method of decision-making. By revealing assumptions, it was hoped that 

stakeholders would perceive and appreciate the work of the agency to weigh benefits 

associated with competing interests with fairness. By revealing assumptions and 

developing conceptual models, this approach also provided a means to allow input by a 

broad range of scientists, managers and the public. 
6 

1.4 Case Study 

For our case study we examined the rangeland invasive cheatgrass (Bromus 

tectorum) which is a management concern throughout the Intermountain West, a large 

area bounded by the Rocky Mountains on the east, and the Sierra Nevada and Cascades 

mountains on the west. This area includes eastern Washington, eastern Oregon, Idaho, 

most of Nevada, and parts of California, Montana and Utah. The boundaries are 

sometimes drawn by characterizing the combined area of the Columbia River Basin and 

Great Basin. Much of our focus was on a sub-region within Southern Idaho that 

corresponded to the management unit whose decisions we were modeling. 

Cheatgrass is a non-native invasive plant with a long and well-documented 

history in this region (Mack 1981, Young and Evans 1978) and serves as a good test 

species because it is thought that this annual grass affects many services by displacing 

native vegetation, and increasing fire frequency and extent (Knapp 1996). The species is 

well-established in the Columbia River and Great Basins, but is not yet at the full extent 

of its range in North America. The species is exceptionally competitive with the native 

vegetation and apparently takes advantage of fires to spread and increase its dominance 

(Knapp 1996, Brooks et al. 2004) although some have questioned this relationship 

(Johnson et al. 2006). 

1.4.1 History and Ecology of Bromus tectorum (aka cheatgrass and downy 

brome) 

1.4.1.1 Native Range of Bromus tectorum 

A synopsis of the biology (i.e., ecology and genetics) and history of the 

introduction of this small annual grass into North America can shed light on various 

aspects of its effect and future influence as well as those tools that could be used to 

control it. Bromus tectorum is a cleistogamous (i.e., almost totally self-pollinating) 

annual grass that occupies an enormous native range in Eurasia and the northern rim of 

Africa (Novak and Mack 2001). It is common, though rarely abundant, all across 

Western Europe, especially in countries surrounding the Mediterranean Sea (Pierson and 

Mack 1990). Its northward limits in Europe are currently in southern Sweden, into which 

it has apparently been expanding its range even in the last century. Eastward it extends 

into all countries in Eastern Europe, including the Ukraine (Tutin et al. 1980). Although 

common in European locales, it becomes more locally abundant on arid, treeless sites, 

encircling the Mediterranean (Upadhyaya et al. 1986). This last point is quite relevant to 

the Intermountain West, which is both arid and largely treeless, except along rivers and 

streams. The pattern of common occurrence but not abundance extends into the Middle 

East, where the grass is reported in a wide swath from Turkey to Rajahistan in Northern 

India. It is also reported to occur in Tibet, and other provinces in western China, 

although its status (native or introduced) is unknown (R.N. Mack, unpublished data). It is 

most abundant in its native range in a region that bears much climatic similarity to the 

Intermountain West – the arid steppes in Turkmenistan and Uzbeckistan. 
7 

1.4.1.2 Pre-adaptation to Environments in the Intermountain West 

B. tectorum appears well suited to the environments in which it occurs. Much of 

its native range is arid, i.e., prolonged dry periods are routine and soil pH may exceed 8.4 

(Daubenmire 1970). The timing of precipitation in such areas is usually unpredictable; 

and, as a result, for an annual species to persist there, it must display considerable 

phenotypic plasticity in response to environmental stochasticity. B. tectorum does indeed 

display enormous plasticity for a wide range of morphological and ecological traits: e.g. 

germination time, rate of growth, number of tillers, and fecundity. Flowering time – 

which is late spring, is one of the few phonological events for which the grass displays 

little site-to-site variation (Rice and Mack, 1991 a, b, c). 

Such phenotypic plasticity for so many traits has direct bearing on the extent and 

persistence of this grass’s invasion in the Intermountain West. Each rainfall event 

triggers a cohort of seedlings within as little as 72 hrs of the site receiving precipitation. 

Thus, a series of cohorts usually emerge from late summer into winter and onward as 

long as the soil surface is not snow-covered. Important here is that practically every 

cheatgrass plant alive on May 1 has produced at least one seed – the basis for the next 

generation (Mack and Pyke 1983, 1984). This remarkably long period of potential 

germination accounts for the difficulty in identifying a season in which control can be 

maximized. Even if control is concentrated in spring, some plants will survive and 

reproduce. 

Other aspects of the biology of B. tectorum, in the context of the Intermountain 

West, explain its proliferation. In autumn, before most of the native species have 

germinated, cheatgrass seedlings rapidly extend their root system deep into the soil 

profile (Harris 1967). Establishment of a deep root system sets the stage for warmer 

conditions in late winter/early spring when these roots undergo further rapid growth and 

usurp the soil water and nutrients (especially nitrogen) before seedlings of the native 

species can become established. Although B. tectorum may offer little competition to the 

adults of the large species in these communities (Artemisia tridentata, Festuca 

idahoensis, Poa secunda), it eventually dominates the site by usurping soil resources 

from successive generations of these species’ seedlings (Harris 1967). Over time, as 

recruitment among these species is effectively truncated, the adult plants, upon death, are 

not replaced in the community and cheatgrass dominates (Daubenmire 1970). 

Furthermore, cheatgrass seedlings can tolerate periodic (but not prolonged) drought, and 

also snow cover and a wide range of soil conditions with respect to texture, salinity, and 

nutrient levels (Mack and Pyke 1984). Cheatgrass is susceptible to many fungal 

parasites, which can devastate populations (Klemmendson and Smith 1964). Most 

serious among these parasites is Ustilago bullata, a smut, which infects the developing 

seed and forms a conspicuous mass of black spores in the aborted seed. Even where the 

vast majority of plants within a cheatgrass population are obviously infected, some plants 

appear immune or at least uninfected. As a result, populations are not completely 

destroyed by this or other parasites (Mack and Pyke 1984). 

Despite its tolerance to an impressive array of environmental forces, mortality 

from drought, ill-timed freezes and voles can be extensive leading to significant 
8 

interannual variability of biomass. Plants that germinate in late summer/autumn run the 

risk of desiccation in September-October if precipitation is not frequent. In winter, chief 

mortality agents are frost heaving of soil peds in which the seedlings have germinated 

(thereby breaking their tap root) and vole grazing. Although cheatgrass can tolerate 

prolonged snow cover, it is susceptible to conditions that produce bare ground (no snow 

fall) accompanied by temperatures well below 0o that freeze the soil. Competition below 

ground for water and nutrients can greatly affect plant vigor, but does not usually cause 

plant death. 

B. tectorum is highly susceptible to competition for light. This vulnerability is 

evident in its native and introduced ranges and is reflected by the fact that this grass 

dominates arid sites that usually have less than 100 % plant cover. As a plant 

community’s canopy coverage approaches 100 %, there is increasing likelihood that 

insufficient light will reach B. tectorum for it to survive. For example, within the 

Intermountain West, B. tectorum reaches its highest abundance in the arid steppe once 

dominated by A. tridentata (Big sagebrush) or on other habitat types that once supported 

communities dominated by other native shrubs (Purshia tridentata, Sarcobatus 

vermiculatus), as well as in somewhat less arid sites co-dominated by Agropyron 

spicatum (Pseudoroegneria spicata) and Festuca idahoensis. 

On the other hand, the ability of B. tectorum to compete is much lower in the 

meadow steppe that was once dominated by Symphoricarpos albus and Rosa 

nutkana/woodsii and a wide variety of broad-leaved perennial dicots (Balsamorhiza 

sagittata, Geum triflorum, Geranmium viscosissimum) (Daubenmire 1970). The grass 

does occur in the forest riverine communities within the Intermountain West, which are 

dominated by Pinus ponderosa, Crataegus douglassi, Salix spp. and Populus trichocarpa

but in comparatively low numbers. It is rare to see abundant cheatgrass along streams 

and rivers in this region, even though these sites would seem to offer ideal growing 

conditions (abundant soil moisture and nutrients). Competition for light intensifies 

within the regional forests, where B. tectorum can occur in low numbers under the open 

canopy within Pinus ponderosa forests, but in forests upslope (beginning with those 

dominated by Pseudotsuga menziesii), the grass is very uncommon (Mack and Pierson 

1990). Light limitation emerges as the chief environmental limitation on the invasiveness 

of this species in the region. 

The grass’s most common habitats in Europe and the Middle East are routinely 

disturbed, either by livestock or human activity. It is common to see B. tectorum within 

or growing beside cereal fields in southern Europe, alongside a road or path or in a 

pasture (R.N. Mack, pers. obser.). In contrast, many of the native angiosperms flower 

infrequently, are poor competitors, do not produce many viable seeds even in the years in 

which they do flower and are intolerant of livestock grazing and trampling (Mack and 

Thompson 1982). In summary, B. tectorum is superbly well pre-adpated (sensu Grant 

1963) to the steppe environments into which it arrived. In some respects, its features and 

traits are superior to those species that evolved within this region. 
9 

Given this grass’s common occurrence in its native range in association with 

agriculture and livestock, it is easy to envision the modes by which it could have arrived 

in the U.S.: as a seed contaminant in agricultural seed (especially the seeds of wheat, oats 

and barley), as a contaminant in any form of dry cargo or ballast (Mack 1981; Mack 

2003). Its long awn (> 1cm) adheres readily to fur or clothing, so it could have arrived as 

a hitchhiker on clothing, although the number of individual seeds arriving in a single 

event via that mode seems to make this mode unlikely. At any rate, the first confirmed 

record of B. tectorum in the U.S. was ca. 1790 in Lancaster, PA (Bartlett et al. 2002). 

Muhlenberg, the doyen of American botany at that time, reports the grass in his Flora 

Lancasterensis (Bartlett et al. 2002). An examination of his collection at the Academy of 

Natural Sciences in Philadelphia by one of the authors (Mack) confirms that Muhlenberg 

had indeed collected B. tectorum. Determining whether any descendants from this early 

population has persisted is problematic because the collection record is silent for the next 

70 years with the single exception of an enigmatic reference to a Bromus sterilis in 

Torrey’s 1843 Flora of the State of New York, for which the description agrees with B. 

tectorum, not B. sterilis. Further searches (by Mack) at the Yale Peabody Museum, the 

Gray Herbarium (Harvard) and the National Museum of Natural History (Washington, 

DC) failed to undercover any pre-1859 specimens. 

1.4.1.3 Spread of B. tectorum to East and West U.S. Coasts and Inland 

The confirmed collection history of B. tectorum – which must always be viewed 

as first detection and not an accurate record of first arrival – is 1859 in West Chester, PA, 

about 80 km from Muhlenberg’s 1790 collection site (Bartlett et al. 2002). It cannot be 

resolved as to whether this small, isolated population found in 1859 stems from the 

population in Lancaster or represents a separate introduction. We do know, however, that 

the collection frequency of B. tectorum quickens substantially after 1859. Mack has 

recently discovered a specimen also collected in West Chester in 1861. Its collection site 

is intriguing – a plant nursery that was actively engaged in receiving and distributing nonnative ornamental species from Europe (Rofini 1986). The nursery’s catalogues from 

1860 onward do not list B. tectorum or any brome for sale (D. Rofini, West Chester 

Historical Society Collection, pers. comm.). Whether this collection was made from a 

population that had arrived as a contaminant in nursery stock or a population that had 

arrived independently of the nursery’s overseas business cannot be determined. The 

strong circumstantial evidence however is that by 1870, at the latest, B. tectorum had 

been introduced repeatedly along the Eastern Seaboard from Philadelphia to Boston. 

Approximately 20 pre-1870 specimens have been examined from sites in this region (e.g. 

Providence, RI; Boston, MA; Philadelphia, PA; Camden, NJ; Long Island, NY; R.N. 

Mack, unpublished data) and provides strong evidence that even if B. tectorum had 

arrived pre-1859 along the Eastern Seaboard, it probably had remained in very small, 

isolated populations. The high level of collection intensity by local botanists and 

naturalists in that era was unprecedented and was certainly higher than the collection 

intensity today. If there had been any more widespread occurrence of this or any other 

non-native species in that region in the mid-19th century, it would have had a higher 

chance of detection than a similar event today. 
10 

By the 1870s, the collection intensity west of the Appalachian approached the 

level in Northeastern U.S. , yet no B. tectorum was reported in the Mid-West (Ohio) 

before 1886. This occurrence was joined, however, in the following decade by multiple 

collections that spanned the Mid-West (R.N. Mack, unpublished data). The collection 

history became trans-continental in the last decade of the 19th century. By 1900 

cheatgrass had been found in Iowa, Colorado, Nebraska and Missouri. The occurrences 

in Colorado and Iowa are coupled with revealing and valuable observations of this grass 

associated with packing straw (Crandell 1893; Pammel et al. 1901). It remains equivocal 

whether the string of pre-1900 collection sites in the Mid-West are all attributable to the 

expansion of the railroad westward, but the pattern of early collection dates through 

Nebraska to Colorado, the route of first trans-continental railroad, suggests that the 

railroad was the chief vector and mode of transport. 

Bromus tectorum arrived in the Intermountain West in the last decade of the 19th

century. The earliest collection of the species was in 1889 in the Okanogan Valley in 

British Columbia, and not much later, in 1893, the species was found in the state of 

Washington (Ritzville). Clusters of other collection dates also occur in eastern 

Washington and Oregon in the years around 1900 (Mack 1981 and R.N. Mack, 

unpublished data). Comprehensive examination of all pre-1900 specimens of B. tectorum

in this study failed to discover any earlier records than those reported in Mack (1981), 

although a full record has emerged with newly-discovered records in Washington and 

Idaho [R.N. Mack, unpublished data]). 

These pre-1900 dates are significant for at least two reasons. Although they are 

contemporaneous with the earliest collection dates in the Great Plains (Iowa and 

Colorado), there are no collection records for the grass in the area, approximately 1000 

miles wide, between eastern Colorado and eastern Washington during the last decade of 

the 19th century. Although it was becoming possible at that time for B. tectorum to have 

been carried by the newly finished railroads across the Northern Rockies into the Far 

West (Mack 1981; Meinig 1968), the lack of any detection of the grass in the intervening 

1000 miles remains curious. Furthermore, the most prevalent genotype of this species, by 

far, in the Pacific Northwest today is termed Got-4c, which has not been detected in any 

other populations in the US, east of eastern Wyoming (Novak et al. 1993). The isolation 

of these early collection dates coupled with the prominence of a unique genotype among 

these populations strongly suggests that plants with the Got-4c genotype entered the 

Pacific Northwest from a route other than across the continent, i.e., they arrived on the 

West Coast and were transported inland. 

Spread of B. tectorum in the Far West, including the Great Basin moved swiftly 

after 1900 (Mack 1981); the pre-adaptation of the grass to the arid environments of the 

region no doubt facilitated this invasion greatly. By 1900, the first records appeared in 

the Salt Lake City area, northeastern Oregon, and many more records appeared in eastern 

and central Washington. By 1915, the arid region of Washington had innumerable 

localities reporting the occurrence of cheatgrass to the extent that it was already being 

recognized as a harmful weed in wheat fields (Mack 1981). Many new farmers to the 

region, in their zeal to claim free farmland from the government, attempted to settle 
11 

claims that had soils far too saline/alkali to support wheat. However, by breaking the thin 

cryptobiotic crust in the sites, experiencing crop failure and then abandoning the land 

altogether, they inadvertently set the stage for rapid occupation of these sites by B. 

tectorum (Mack 1981). Habitat types with this soil chemistry (and fate) are the 

Sarcobatus verminculatus/Disticlis stricta and Grayia spinosa/Distichlis stricta

(Daubenmire 1970), which are primarily in south-central Washington, which is the most 

arid portion of the steppe in Washington; similar communities occur farther south in the 

region. 

If B. tectorum first advanced into the Intermountain West from west coast points 

of disembarkation (Puget Sound and the mouth of the Columbia River), what role did 

California ports play as early points of introduction? Apparently, any role these early 

major ports played in the grass’s spread occurred later and does not appear to have 

contributed the Got-4c genotype of this species that is so prevalent today. One of us 

(Mack) has now examined all the B. tectorum collections at university and other herbaria 

in California (e.g. UC Berkeley, Humboldt State, Fresno State, Rancho Santa Ana 

Botanical Garden, California Acad. Of Sciences) and found no pre-1900 collections. Nor 

do any pre-1900 journals or articles by plant collectors in that region mention B. tectorum

Mack has now examined these journals (e.g., Zoe and Hilgardia) through the relevant 

years, and although “no detection” cannot be unequivocally equated with "no occurrence" 

(Mack 2000), the relatively strong collection intensity in California in the decades around 

1900 suggests that the grass had not yet arrived. 

In the late 19th and early 20th century San Francisco, and soon thereafter Los 

Angles, became home to numerous amateur, but nonetheless knowledgeable, plant 

collectors. Recognizing that they resided in a region with a poorly known flora of both 

native and introduced species, and further recognizing that new introduced species were 

continually arriving, a cadre of eager plant collectors combed the streets of San Francisco 

looking for new plant to report. These collectors routinely (and much more often than 

yearly) reported the new findings from their surveys of the burgeoning cities of 

California. In many cases, their collections survive and can be annotated. The earliest 

California specimen of B. tectorum is dated 1899 (R.N. Mack, unpublished data) – and 

was collected in northern California, far removed from the metropolitan ports. This 

suggests that this collection may represent the southward spread of B. tectorum from the 

North (the Got-4c genotype) rather than representing the early entry of the grass in 

California and its spread northward. Collections of the species do appear with increasing 

frequency in northern California and at Santa Barbara, a seaport, 1900-1908. 

Entry of B. tectorum via San Francisco does likely explain another genotype that 

eventually reached the western fringes of the Intermountain West near Reno, NV. Mack 

has traced this genotype (Pgi-2b) to its native range in southern France and the Iberian 

Peninsula. It is not surprising hat B. tectorum would have immigrated from that part of 

the Mediterranean to California, given the long association of California with Spain. It is 

surprising that the first American botanists in California, who arrived in the latter half of 

the 19th century, did not report detecting B. tectorum. Nevertheless this genotype is 
12 

common around Truckee, CA and Reno, NV; yet has not spread widely into the Great 

Basin; which is anomalous. 

The invasion of B. tectorum in the Intermountain West followed a common 

trajectory of a lag phase (about 20-25 years) in which range expansion began from a few 

isolated locales within a restricted area, followed by a logistic growth phase (15-20 years) 

in which range expansion accelerated, such that most of the habitat in which B. tectorum

could persist was occupied by ca. 1930. Given the grass’s attributes discussed above 

(successively germinating cohorts, enormous phenotypic plasticity, ability to usurp soil 

resources, tolerance of grazing and trampling, tolerance of frequent fire), its spread was, 

in retrospect, not surprising. Collectively these traits allowed B. tectorum to transform 

the steppe communities in the Intermountain West within no more than 45 years (ca. 

1890-1935) and within probably less than 25 years (ca. 1910-1935) (Mack 1981 and 

unpublished data). 

1.4.1.4 Ecological Genetics of B. tectorum in the Intermountain West 

Two genotypes, reflecting at least two independent introductions of B. tectorum to 

the region, brought about most of this transformation. Of these, the aforementioned Got4c genotype was likely most responsible, followed by a genotype that is widespread in 

western Europe (MCG). Two other genotypes (the aforementioned Pgi-2b) and a trace 

occurrence of a fourth genotype (Mdh-1b/2b) are also present but in isolated areas. The 

role of the Got-4c genotype is remarkable because its native range in Europe is quite 

restricted. Based on approximately 150 populations that have now been examined, the 

Got-4c genotype is restricted to a small area in eastern Germany and the adjacent portion 

of the Czech Republic. The climate in this region, while perhaps the most arid in 

Germany, is hardly similar to climates in the Intermountain West. And yet, in common 

glasshouse experiments, this genotype consistently showed high vigor and fecundity 

when compared with other genotypes from Western Europe, including the widespread 

MCG genotype (Novak and Mack, 1993; 2005). 

Ironically, the Got-4c genotype that invaded the Intermountain West is 

comparatively vigorous. In extensive common glasshouse experiments Kinter (2003) 

demonstrated that these populations were likely composed largely, if not totally, of plants 

with the Got-4c genotype and were superior in a wide array of growth features to plants 

with the MCG genotype. The putative Got-4c plants ranked first in phonologic 

development germination, tiller growth, tiller number (a strong correlate for eventual 

plant fitness), panicle number, panicle biomass, vegetative biomass, and total biomass. 

In other words, the putative Got-4c plants from the Intermountain West emerged sooner, 

grew faster and taller, produced more biomass and ultimately more flowering panicles 

than plants of any of the other sources examined in the side-by-side trials. Not only was 

the Intermountain West invaded by a grass that was pre-adpated to the region's 

environment, it was invaded by the most vigorous and fecund genotype of this 

widespread Eurasian grass that has yet been detected. 
13 

1.4.1.5 Cheatgrass and Its Role among the Steppe Communities 

Bromus tectorum is primarily an invader of the steppe (i.e., those grasslands 

dominated by perennial grasses) in the Intermountain West. This is a reflection of the 

strong tolerances and vulnerabilities that the grass displays, including highly tolerance for 

periodic drought, low soil nutrient levels, saline/alkali soils, snow cover, repeated 

grazing, routine disturbances of the soil surface, and microbial parasites. The species, 

however, is vulnerable to prolonged bouts of frozen, bare soils and competition for light. 

These species characteristics provide signals that can be used to predict sites on which it 

has proliferated as well as sites from which it is largely precluded. 

The steppe communities of Washington illustrate the environmental spectrum of 

sites in the Intermountain West across which B. tectorum shows substantial variation in 

abundance. In general, B. tectorum is most abundant on those sites that are most arid 

(<250 mm annual precipitation). As a result, the grass is a clear dominant in the arid 

steppe (e.g. A. tridentata/A. spicatum zone); almost as dominant in the steppe in eastern 

Washington displaying the co-dominance of A. spicatum and F. idahoensis. The grass is 

also common, but usually not abundant, within the meadow steppe zone (S. albus/F. 

idahoensis) which receives the most precipitation (> 350 mm) and forms the lower 

timberline ecotone with P. ponderosa communities at characteristic elevations 

(Daubenmire 1970). The lower prominence of B. tectorum in the meadow steppe habitats 

is also attributable to the intensive cereal agriculture in this zone, which involves routine 

herbicide treatment for cheatgrass. Further west (A. tridentata/A. spicatum and A. 

spicatum and F. idahoensis zones), farming is less prevalent and much more of the 

landscape is devoted to livestock rearing. In addition to supporting native communities 

that have low canopy cover (the chief limitation for cheatgrass), these economically 

marginal lands do not usually receive herbicide treatments. It is the large areas in the 

Intermountain West that support the arid steppe environment, now dominated by 

cheatgrass, that present the most difficult areas in which to attempt any program to 

control, much less eradicate, this species. 

Cheatgrass is one of several plant invaders on agroecosystems of the 

Intermountain West and appears to be part of a trend of irreversible changes in plant type 

and structure that adversely impact a range of valued ecosystem services including those 

supporting agricultural productivity. The primary mechanisms by which ecosystem 

services are impacted are through direct habitat loss and indirectly through enhanced fire 

frequency. The specific links between ecosystem services and welfare changes are 

discussed below. 

1.4.2 Burned Area Rehabilitation and Emergency Stabilization and Rehabilitation 

Programs 

The specific management decision we modeled involved prioritizing the 

allocation of funds within Burned Area Emergency Stabilization and Rehabilitation 

programs in southern Idaho. In these and similar rehabilitation programs, burned areas 

are rehabilitated through seeding and other activities to prevent erosion and promote the 

establishment of desirable species. In areas where cheatgrass is present, treatment is 
14 

undertaken to prevent the species from taking advantage of the disturbance in order to 

quickly establish and become dominant before native species have the opportunity to 

rebound. Cheatgrass infestations in the Intermountain West are typically managed jointly 

by Bureau of Land Management and USDA Forest Service, so similar techniques are 

used in both agencies. Managers at BLM were willing to share databases with us, so we 

focused on decisions made by BLM in the Twin Falls District of Southern Idaho (Figure 

1). The types of decisions this management unit must make are typical of many other 

natural resource agencies who receive funds from this program or similar programs. 

The post-fire period appears to be the most important time to treat since 

cheatgrass and other annual invasive grasses are well-adapted to fire and take advantage 

of this disturbance to increase their extent and dominance. A fairly low level of 

cheatgrass cover, can rebound post-fire to become the dominant species. Cheatgrass 

survives these recurring fires via its buried seeds, which have been produced before onset 

of the fire season. In contrast, many of the native herbaceous perennial species and 

native woody species, such as Artemsia tridentata, are eliminated from these sites by 

cheatgrass fires (West and Yorks 2002). Within a few decades, any site with prominent 

coverage of cheatgrass is converted to complete dominance by cheatgrass (Knapp 1996; 

Evans et al 2001). 

Figure 1. Site Map of BLM Twin Falls District in Southern Idaho 

Boundaries of management unit used in case study. 

1.4.3 Treatment Options 

Ideally, a cost-effectiveness analysis should address the full range of management 

options to directly or indirectly generate benefits, typically through damage avoided. 

While the strategies that we will address here involve primarily direct options, some 

indirect strategies may also be appropriate to prevent harm. For example, if the primary 

concern with cheatgrass were enhanced risk of fire to property, an appropriate indirect 
15 

management action might be to fund programs that created incentives for property 

owners to use fireproof materials in buildings. 

The full range of direct options for addressing an invasive species problem include: 

1) Ignore No response. 

2) Monitor Routinely measure the intensity and extent of the weed threat. 

3) Contain Prevent a weed that has already been introduced to a region from 

spreading to new areas. 

4) Control Remove weeds and limit their growth in areas already infested. 

5) Eradicate Implement control until the weed, seeds and propagules are 

eliminated from infested areas. 

6) Mitigate Offset the effects of the weed infestation, for example, by 

creating, restoring, or enhancing alternative wildlife habitat. 

7) Adapt Allow businesses and households to respond as best they can to 

the spread of weeds; this may be a no-response option associated 

with an unavoidable weed threat (e.g., when human disturbance 

is likely to result in reinfestation, or when no acceptable 

treatment method is available). 

For direct cheatgrass control following fire, treatment options available to managers 

include various seeding techniques combined with physical manipulations and/or 

herbicide treatments. On rare occasions, sites may be hand planted with seedlings. For 

purposes of our analysis, we defined five levels of treatment (including no treatment) that 

represent increasing intensities of effort (person-hours and spending) that could be 

directed at a given burned site. The management decisions being addressed, in other 

words, involved choosing which of the five level of treatment intensities to apply at 

various fire sites, subject to constraints on budget, person-hours, and other factors. 

Cheatgrass Treatment Options

1. No treatment 

2. Aerial seeding only (mix of native/non-native) 

3. Aerial seeding + chaining 

4. Aerial seeding + chaining + herbicide 

5. Aerial seeding + chaining + drill-seeding 

Aerial seeding involves the placement of seeds on burned areas from small fixedwing aircraft or helicopters. Chaining is a technique used to increase soil-seed contact 

and enhance germination, but can only be used where sites are accessible to tractors. 

Herbicide treatments may be conducted with hand sprayers or aerial application. Drillseeding involves use of special equipment that digs, furrows, drops, and then covers 

seeds. Drill-seeding enhances germination rates, but is typically applied over small areas, 

and can only be applied where slopes are gentle and where areas are accessible by tractor. 

While treatment techniques may be mixed and matched in different combinations, 

managers typically apply a low, medium, or high intensity effort to sites based on 

expected benefits. The specific combinations of techniques listed above are typical, and 
16 

are used in our analysis as proxies for intensities of treatment effort because doing so 

allowed us to use actual cost and effectiveness data and information in our analysis. 

An important decision the manager must make is whether to place native or nonnative seeds on a rehabilitation site. The non-native species used include perennial 

grasses such as crested wheatgrass which have much higher germination rates than native 

perennial grasses. They offer benefits such as high quality forage and some ability to 

withstand cheatgrass invasions, but do not offer the same habitat benefits for some native 

species and are not as well adapted to severe droughts as the native species. The native 

species, on the other hand, have low germination rates, are generally more expensive than 

non-native species, and do not offer much resistance to cheatgrass on disturbed sites. 

However, the range of native shrubs has been significantly reduced as a result of the 

invasion of non-native species. Managers have a goal to retain and restore this 

characteristic vegetation that supports many native birds that annual grasslands cannot. 

A technique we did not consider in our analysis but which warrants further 

investigation is the use of “flash grazing” or “targeted grazing” where sheep or cattle are 

stocked at high rates for short periods in order to reduce aboveground portions of all 

vegetation. When applied at the proper time of year, this technique has the potential to 

reduce annual grass populations and favor native perennial grasses (Mosley 1996, 

Davison pers. comm.). The technique is highly controversial due to the potential for 

permanent harm to soil crusts and sensitive ecosystems, but appears to be a cost-effective 

method of cheatgrass control that may be appropriate for systems where soil crusts are 

not present, habitat is degraded, or other methods of treatment can not be applied, such as 

rocky areas. Evidence suggests the technique is successful at controlling cheatgrass in 

the year it is used and the subsequent year, but treatment must be repeated to achieve 

ongoing success (Davison pers. comm.). Long-term studies have not yet been conducted 

to evaluate potential for long-term control. 

1.4.4 Framing the Benefits Assessment 

As a widespread invasive that “cheated” wheat farmers out of their expected crop 

yields decades ago, the impact of cheatgrass on human welfare is relatively well 

understood compared to most invasive species. Yet, the magnitude of the harm is not 

well constrained for many ecosystem services. Cheatgrass is thought to create harm by 

displacing native plants and altering plant type and structure, which leads to associated 

changes in ecosystem functions such as soil nutrient storage and fuel conditions (Brooks 

et al. 2004). Functional changes result in habitat losses for certain species and changes in 

the system’s fire dynamics. Fire is a natural component of much of the Intermountain 

ecosystem we investigated, although some evidence suggests that fire recurrence interval 

and extent has increased since the spread of cheatgrass and other annual grasses. 

As an annual plant, cheatgrass dies immediately after maturation of the next 

generation’s seeds. This maturation coincides all across the Intermountain region with 

the onset of summer drought. With little or no rain from mid-June until mid-September, 

cheatgrass adults rapidly die. These dead plants are highly combustible and the 
17 

monocultures of cheatgrass that have arisen across much of the area create a large fuel 

load. High air temperature, low rain, and the potential for high winds in summer create 

ideal and recurring conditions by which these masses of fuel ignite and burn rapidly. In 

contrast to cheatgrass, the native species mature later and maintain green vegetation later 

into the summer, thereby shortening the period of dry vegetation. The later date of seed 

set means natives are more easily eliminated from sites during fires. 

An important distinction between a landscape dominated by native perennial 

grasses and shrubs and annual invasive grasses such as cheatgrass and medusahead 

(Taeniatherum caputmedusae ssp. asperum) is the patchiness of the landscape. The 

native grasses, referred to as “bunch grasses” form clumpy patches on the landscape in a 

matrix of shrubs and bare ground. This patchiness is thought to reduce the extent of fires 

relative to landscapes dominated by invasives grasses, which tend to form a more 

continuous landscape of grasses (Pyke et al. 2003). 

The evidence for increased fire frequency due to cheatgrass is somewhat 

circumstantial and anecdotal (Roberts 1990, Stewart and Hull 1949, Whisenant 1990). A 

recent formal study (Pyke et al. 2003) may be the first to quantitatively assess the change 

in fire frequency due to invasion by annual grass. Their evidence suggests at least a 

doubling of fire risk in the recent past where cheatgrass cover is dense and a four-fold 

increase in average fire size, and earlier workers suggested a risk of fire 10-500 times 

higher in cheatgrass-infested rangelands, requiring 5 times the resources to control (Hull 

1965 cited in Roberts 1990). 

The prime evidence for increased fire frequency seems to be that the nature of a 

cheatgrass infestations (dense production of fine-textured biomass that matures and dies 

earlier than native vegetation) creates a landscape that is more prone to burning, increases 

the fire season for almost 2 months, and increases the probability that native species will 

be harmed by fire (Knapp 1997, Young and Blank 1995). Regardless of the ability to 

document change in fire frequency, what seems clear is that cheatgrass is a fire-adapted 

species that is able to take advantage of fires to increase its dominance of the sagebrush 

landscape, thereby suppressing native vegetation growth (Young and Evans 1978). 

The enhanced risk of fire due to cheatgrass presence and spread may never be 

defined because, unlike forest fires that leave scars on trees, grassland fires do not leave 

evidence that can be retrospectively evaluated (Young and Blank 1995). No method for 

evaluating historic fire frequency in grasslands that lack trees has been developed, to our 

knowledge. Simulation models have shown that fire extent is sensitive to fuel 

fragmentation and load (Duncan and Schmalzer 2004) suggesting that the more 

continuous cover of cheatgrass would be predicted to increase fire extent relative to the 

patchy cover of the native grass and shrublands. 

A recent report has suggested that there is insufficient evidence to reject the null 

hypothesis that abundance of invasive plants is not changed by wildfire (Johnson et al. 

2006). This report combined data from the peer-reviewed literature on several invasive 

grasses and forbs in several ecosystem types in an effort to establish a statistically 

significant effect of fire on non-native species abundance. Unfortunately, poor data 
18 

quality limited their ability to draw firm conclusions. Many studies they found had small 

sample sizes, short duration, or used sites with substantially different landscape contexts, 

making it difficult to draw conclusions given the high natural variability of the systems. 

The authors document a disturbing tendency on the part of researchers to claim an effect 

on non-natives when evidence is mixed or variable. However, the evidence to reject the 

null hypothesis appears as weak as the evidence suggesting an effect, particularly for 

sagebrush areas. While the scientific method requires preserving the null hypothesis in 

the absence of evidence to reject it, decades of observational evidence must carry some 

weight when the quantitative evidence is poor. 

Because we had no firm evidence to contradict the widely-held belief that 

cheatgrass cover is increased by fire and in turn leads to enhanced fire frequency, we 

accepted the common wisdom of our management partners for purposes of developing 

our analysis. If this assumption is later proven to be invalid, then the relative benefits of 

cheatgrass management and the spatial pattern of benefits will likely be misrepresented 

here. In particular, the benefits assessment for commercial forage production and 

property protection are highly sensitive to the assumption that cheatgrass reduces the 

duration of the fire-free interval. On the other hand, for benefits derived from changes in 

habitat, namely those derived from hunting and existence values, only modest changes in 

relative benefits might be expected if this assumption proves to be invalid. Treatments 

aimed at preventing cheatgrass dominance still improve on-site conditions for these 

services and reduce the chance of cheatgrass spreading to uninfested habitat. 

1.4.5 Potential Welfare Changes with Cheatgrass Spread 

To inform our selection of benefit indicators, we first evaluated potential welfare 

effects from cheatgrass spread. Our final analysis did not evaluate these welfare changes 

explicitly in a cost-benefit framework, but the framing of the benefits is important to 

correctly identify potential impacts on valued ecosystem services. A full assessment of 

monetary impacts to conduct a cost-benefit analysis would require prohibitive levels of 

resources from resource management agencies. However, managers may find this 

discussion of welfare effects (as opposed to purely ecosystem service changes) as useful 

for informing choice of ecosystem services to consider when describing and measuring 

program benefits. 

A variety of changes in ecosystem services result from cheatgrass becoming a 

dominant species in agro-ecosystems of the Intermountain West, and many of these 

changes can be linked to impacts on human welfare. Effects on ecosystem services were 

identified through a literature search and interviews with government managers, 

agricultural extension agents, researchers in academic and government institutions, and 

private businesses. We evaluated these effects on ecosystem services to identify potential 

impacts on social welfare (Table 1) and eventually narrowed the focus of our work to 

four main types of services that appeared to be the primary pathways by which cheatgrass 

adversely affects people. 
19 

Some potential benefits of cheatgrass were also identified for recreators and 

commercial ranchers. For example, off-road vehicle (ORV) users take advantage of 

burned areas and therefore appear to derive benefits from increased frequency or extent 

of fires. However, ORV users also avoid cheatgrass-infested areas at certain times of the 

year in order to avoid starting fires (M. Pellant, pers. comm.). Therefore, benefits of 

using burned areas were at least partially offset by the inconvenience of avoiding 

cheatgrass infestations. Due to the relatively small size of the net benefits, the potential 

benefits of cheatgrass were not included in the optimization model. 

The effect of cheatgrass on commercial forage production is mixed. Ranchers are 

able to use cheatgrass-infested areas for grazing in the spring and the forage quality at 

that time can be superior to native species, particularly if the cheatgrass is less than 50% 

of cover. The fact that cheatgrass dies off earlier than native species is not a significant 

problem in parts of the study area because ranchers must typically move cattle to higher 

elevations (above the zone of cheatgrass infestation) in summer to find water sources. 

Currently, cheatgrass is not widespread at elevations above 5000 feet (Pierson and Mack 

1990) however, a new cheatgrass genotype may have emerged that seems to be able to 

dominate at high elevations (Brown and Rowe, in press). Cheatgrass productivity is 

thought to be less consistent than native vegetation since it is more susceptible to drought 

than natives (Roberts 1990). 

Despite the lack of direct harm to forage quality at low percent cover, ranchers 

appear to have growing concerns about systems becoming dominated by cheatgrass (M. 

Pellant pers comm., various agricultural extension websites) because of the direct impacts 

of fire on their operations, the loss of late spring-summer grazing areas, and a perception 

that annual grasses such as cheatgrass have more variable production than perennial 

species. Fire appears to have the most direct adverse impact on ranchers leasing land. If 

a grazing allotment is burned, it is BLM policy to prevent ranchers from using the land 

for 2-3 years while the land recovers. The effect of BLM’s policy toward lessees on 

individual producer profits depends on whether the rancher has alternative allotments to 

use, and how well he can adapt by changing stocking rates or buying/producing 

supplemental feed. Ranchers are generally opposed to this policy of being removed from 

the land, indicating that they see an adverse impact of fire, or, more specifically, of 

government's response to fire, on profits and/or their personal welfare. Other evidence 

that ranchers are increasingly worried about cheatgrass spread is the development of 

private associations of ranchers and others that are aimed at controlling cheatgrass (M. 

Pellant, pers. comm.). 

Anecdotal evidence from managers and ranchers indicates that the variability of 

forage production can be greater when a system is dominated by annual grasses, such as 

cheatgrass, as opposed to perennial grasses. Such a claim is supported by ecological 

principles that predict higher variability of biomass production in an annual plant species 

relative to a similar perennial species, over the long term. Research also supports the 

concept that cheatgrass can have variable productivity year to year and plot to plot 

(Bradley and Mustard 2005, discussion in Johnson et al. 2006). In the end, we identified 
20 

the primary effect of cheatgrass on commercial ranching profits as the lost profits of 

being removed from the leased grazing allotment for a 2-3 year period. 

The effect of cheatgrass on hunting opportunities is similar to the ranching story. 

Many popular game species are able to use areas dominated by cheatgrass, implying little 

to no welfare effects from post-fire treatments.1

 However, two hunted species appeared 

to be directly at risk from cheatgrass: antelope (Antilocapra Americana) and sage-grouse 

(Centrocercus urophasianus). These species do not readily use cheatgrass-dominated 

areas and therefore require native vegetation to thrive. Neither species is listed as 

threatened or endangered. However, managers anticipate future problems for these 

species since their habitat areas are shrinking and populations of sage-grouse appear to be 

declining from historical levels. The conservation status of sage-grouse is considered 

“near threatened” (BirdLife International 2006). In addition, managers expressed some 

concern that deer overwintering habitat was also threatened by cheatgrass since deer 

move to low elevation in winter and cheatgrass that dominates at these lower elevations 

does not provide any food value for deer at that time of year. However, the deer 

population appears stable for the moment, so the degree of this threat is not clear. 

A list of ecosystem services that we identified as being affected by cheatgrass is 

provided in Table 1 which includes a brief description of the mechanism by which 

cheatgrass infestations are thought to induce welfare changes. The specific ecosystem 

services that were the focus of attention in our benefits analysis are shown in Table 2. 

 

1

 Cheatgrass dominated areas are widespread and plentiful, so hunting opportunities are not lost by treating 

cheatgrass areas. Popular hunting species that use such areas, such as the chukar (Alectoris chukar), are 

generally abundant and, for the chukar, the conservation status is “least concern” (BirdLife International 

2005). 
21 

Table 1. Potential Welfare Impacts of Cheatgrass 

Ecosystem 

Service Category 

Mechanism of Welfare Change Potential Impact on Welfare 

(consumer or producer surplus) 

Hunting (sagegrouse, antelope, and 

potentially mule 

deer) 

Fires destroy habitat & reduce resilience 

of populations/herds. 

Loss due to: increased costs of access, 

reduced bag rates, reduced quality of 

experience. 

Hiking / Dog 

Walking 

Generates time of year restrictions on 

natural area use since seeds are a 

nuisance to dogs and people. Animals 

get infections from embedded seeds 

which require operations to remove. 

Loss due to: increased costs of access 

since users avoid infested/burned areas; 

reduced quality of experience. 

All terrain vehicle 

use 

Users avoid when fire-prone, but 

burned sites are preferred. 

Potential gains or losses due to 

increased access of burned areas or loss 

of access in fire-prone areas. 

Property protection Increase in fires Private or public losses associated with 

increased costs for fire prevention (e.g., 

building requirements), property 

replacement, and higher insurance rates. 

Health Risks Increase in fires cause undesirable air 

quality which can trigger health 

problems (Ferguson et al. 2003) 

Losses due to increased incidence of 

disease and health care costs or 

insurance rates; lost worker 

productivity. 

Aesthetics Burned areas offer degraded views and 

wildlife are displaced. 

Losses due to reduced quality of views 

and lost wildlife viewing opportunities 

associated with driving or recreation. 

Soil Stabilization Fires create erosion events that can 

block roads and degrade stream habitat 

(includes degradation of salmon 

spawning areas) (Klemmendson and 

Smith 1964; USACE 2002) 

Losses associated with public costs to 

remove material. Effects on salmon 

difficult to characterize as losses 

because other stressors on populations 

dominate. 

Existence values Sagebrush (Artemesia) and sage-grouse 

(among other species) are displaced by 

cheatgrass and are becoming 

increasingly scarce. Widespread loss of 

sagebrush in this area appears 

irreversible without human intervention 

(Whisenant 1990) particularly in salt 

desert communities where natural fires 

were historically rare. Raptors are 

indirectly affected through loss of 

rodent population (Brooks et al. 2004, 

US DOI 1996) 

Losses due to diminished population of 

characteristic valued species. 

Producer losses by 

ranchers 

Increased fires. Fires reduce 

productivity and/or increases costs. 

BLM policy is to shift ranchers off 

burned areas for 2-3 years. Without fire 

- increased variability of forage; costs 

associated with seeds becoming 

embedded in animals. 

Lost producer profits if ranchers have 

no substitute land after fire. Potential 

reduction in profits from having to 

provide supplemental feed or reduce 

herd size. 
22 

Table 2. Ecosystem Services Used in Benefits Analysis 

Benefit Variable Service Description 

b1 Recreational Antelope Hunting 

b2 Forage Production for Commercial Ranching 

b3 Property Protection (public and private) 

b4 Habitat Support for Sage-Grouse (characteristic species) 

1.4.5.1 Off-Site Benefits of Site Treatment 

Treatment at a site not only improves on-site conditions for providing certain 

ecosystem services and related benefits, but also improves the expected future streams of 

services and benefits from neighboring sites by preventing their infestation or reducing 

the risk of fire. To capture the relative level of protection to neighboring sites of treating 

any particular site, we relied on measures of landscape connectedness. Our assumption 

was that a site would be more likely to confer advantages to other sites if it were wellconnected (ecologically and biophysically) to areas showing no cheatgrass cover. The 

degree of connection was measured using landscape metrics described in Section 3.2.2. 

2. Problem Formulation 

Conceptually, the manager’s decision problem is to choose specific sites to treat 

and specific intensities of treatment at those sites so as to maximize change in total 

benefits subject to a budget constraint. In practice, only a small proportion of sites can be 

treated with the available budget. When different services cannot be provided 

simultaneously at the same site, the manager must make tradeoffs among services and the 

services are considered antagonistic. On the other hand, if services are complementary

and treatment of a site enhances all services simultaneously, the manager may be able to 

maximize aggregated benefits without having to explicitly trade-off services. In our 

formulation of the problem, we employ a weighting scheme that assigns relative 

importance to different services, providing a means to trade-off services when 

aggregating benefits. The service weights must be the same for all individual sites, but 

since different sites will have different capacities to enhance particular services, these 

weights can have proportionately different effects on the overall benefits from treating 

different sites. 

Many potential treatment sites must be compared for cost-effectiveness. In Idaho 

alone, over a three-year period (2001-2003) about 4000 fires burned on all lands while 

only 50 or so were treated on BLM lands under the two programs we examined: 

Emergency Stabilization & Rehabilitation and Burned Area Rehabilitation (Figure 2). 

We used information for 46 of the treated fires over the three-year period to evaluate 

treatment spending patterns. 

Within BLM, managers within a given district office (sub-state level) must decide 

each year which fires within their district will be treated. For the Twin Falls District that 
23 

we were modeling, in 2002, 114 fires were recorded on BLM lands. In our costeffectiveness analysis and optimization modeling, we compared in detail 68 of those fires 

that had been mapped within the GIS database of fire occurrences and that were larger 

than one acre. 

2.1 Optimization Model Overview 

A generalized version of the optimization model can be summarized as follows: 

Let Bt equal the aggregated net benefits at time t of improvements in the set of ecosystem 

services j from treating a set of sites i with treatment k2

 where bijk is a vector of services 

(bi1k = recreational antelope hunting, bi2k = forage for commercial ranching, bi3k = 

property protection, and bi4k = benefits associated with sage-grouse) and aggregate net 

benefits (Bt) are calculated as: 

Bt = ∑∑ ( ) − i j

without

ijk

with w (Eqn 1) j bijk b

bijk = benefit, with or without treatment 

 wj = weight applied to service j 

 i = location i, (sum over treated subset of burned sites)

 

2

 Note that treatment may result in improvements of some services at the expense of other services, so the 

direction of change in benefits with treatment is not necessarily positive. 

Figure 2. Treated and 

Untreated Fires 2001-2003 

Fires shown in yellow, orange or red 

were treated under Emergency 

Stabilization & Rehabilitation and 

Burned Area Rehabilitation 

programs in Idaho in 2001-2003. 

Blue dots are fires of any size 

occurring during that same period, on 

any public lands, that were not 

treated in these programs.
24 

 j = service j (sum over service benefits : recreation, forage, property protection, 

existence values for sage-grouse) 

 k = treatment intensity applied

Benefits are evaluated at a single point in time, 2-3 years following restoration. 

The budget constraint is set to the allocated program budget and cost of treating a 

site is calculated as: 

TCik = k i TCAik Ai FC + JC * JT + * (Eqn 2) 

FC = Fixed Costs

JCk = Journey (Travel) Cost, personnel and equipment 

JTi = Journey Time (hours) 

TCAik = Treatment Cost per Acre 

 Ai = area treated (acres) 

The factors under control of the manager are: 

i = site treated 

k = treatment applied to burned area i (expressed as treatment intensity level)

w = weights assigned to benefits j 

The treatment intensity, k, includes the use of multiple trips to sites and costs reflect both 

inputs per trip and number of trips. 

2.2 Short vs. Long-Term Benefits Analysis 

Benefit calculations can be conducted over a short or long time period. In the 

world of natural resource decision-makers, social benefits are generally maximized when 

the expected future stream of benefits is maximized. Someone making an investment in 

preserving or restoring a natural asset typically wants the investment to pay out over 

some period of time. For this analysis, we set a single evaluation point for benefits of 2-3 

years following treatment, to increase the tractability of the system for use by managers. 

Managers can reasonably evaluate short term success of a restoration treatment 2-3 years 

following rehabilitation and, from that short-term success, can infer potential long-term 

success. We recognize that the use of a single short time-frame in the benefits equation, 

while a great advantage for simplifying calculations, may emphasize short term gains 

over long-term results.3

 

To counteract this apparent emphasis on the short-term, we incorporated two 

approaches in calculating net benefits to reflect long-term impacts of treatment. The 

main approach was to define benefits in terms of the change in the percent invasive cover 

and to limit benefits to less than 100% of maximum, even if 100% native cover would be 

expected at the post-treatment evaluation 2-3 years following treatment (see detailed 

discussion of benefits function below). Short-term gains in native plant cover are 

expected to translate into higher likelihood of long-term benefits (e.g., in terms of species 

survival and preservation of hunting options), but full potential benefits would not be 

 

3

 By comparison, a multiple time period or dynamic analysis would allow us to project benefits in each of 

many future time periods, apply a discount rate to future benefits, and examine residual land values at the 

end of the time horizon to better model investment decisions. 
25 

realized at that point in time. Using this construct, the benefits function reflected the 

concept that some benefits would not be realized until native cover was maintained over 

some future time frame (e.g., 30 years hence). 

A secondary approach to reflect potential future benefits was to include a term in 

the benefits calculation that projected the importance of a site for preventing spread of 

infestations to neighboring areas. This term was an indication of the persistence of 

benefits, produced by neighboring sites, that would be maintained by treating site i. In 

other words, treating the site of interest would be expected to slow or prevent infestation 

of neighboring sites, or reduce the risk of fire to neighboring sites, thereby allowing those 

sites to produce a greater flow of benefits over the long-term. 

3. Benefits Assessment 

Our method to assess benefits of treatment relied on indicators of benefits and did 

not directly quantify economic value of services in monetary terms. The endpoints we 

measured were evidence of changes in economically important ecological services, but 

had limitations in terms of being able to quantify probable use, substitution among sites, 

and user benefits. We recognized these limitations, but expected that this system would 

provide adequate information about benefits to enhance decision-making by resource 

managers and potentially increase economic efficiency of resource allocation decisions. 

The main difference and advantage of an indicator system of benefits rather than a 

system of biophysical endpoints (such as number of sites, or acres of grazing area) as a 

management target, is that the system incorporates components of asset quality, scarcity 

and value. Although the analysis is not without its judgments about preferences, the 

value judgments are made explicit and we reveal assumptions about relative values that 

are inherent in resource allocation decisions but not always made explicit. 

The approach to measuring benefits of treatment that we used resulted in benefit 

indicators that were site-specific and took into account spatial heterogeneity of land cover 

and land use both on and in the vicinity of burned areas. Quantifying relative benefits at 

a particular site involved several steps. The description of our benefit estimating 

approach below progresses from the general, what we were trying to measure, to the 

specific, the equations and relationships we used to calculate relative benefits for each 

case of site and treatment intensity. We also describe how benefits were risk-adjusted 

using expected outcomes and different types of benefits weighted to reflect management 

goals. 

3.1 General Benefits Model 

Let bijk, the benefits from service j of treating a given burned area i at treatment 

intensity k, be a function of the maximum possible benefits from the site in the absence of 

invasive species, max

ij b , the site restorability or treatment effectiveness, Sik, and the off-site 
26 

benefits derived from protecting neighboring sites from infestation or reducing the risk of 

fire in neighboring cells in any given year, Ci. 

 bijk = f ( max

ij b , Sik, Ci, Ai) (Eqn 3) 

max

ij b = maximum possible site benefits at site i for service j

Sik = restorability outcome, measured as % native vegetation, for a given site 

and treatment level 

Ci = contribution to maintaining off-site benefits, measured as the effect of 

the site on contiguity / connectedness of native vegetation 

Ai = size of treated area 

Benefits derived from treatment are thus defined as a function of innate site 

characteristics that affect expected change in benefits in three ways. First site and 

landscape characteristics are used to measure a maximum potential level of benefits, max

ij b

(in the absence of invasive species). Second, site and landscape condition determine the 

site’s ability to recover post-fire (recoverability), the outcome of treatment (restorability) 

and the difference between the two, which is used to generate net benefits. Finally, the 

protection conveyed to existing sites from treatment is quantified in terms of a descriptive 

statistic of land cover spatial pattern, Ci, that is essentially a proxy for invasion or fire risk 

to neighboring lands. See further description below. 

The site restorability, Sik, was measured as the estimated percentage of native 

vegetation cover post-treatment. The estimation of Sik is described in Section 5. 

Unfortunately, little empirical information was available to judge the expected 

relationship between how ecosystem service benefits changed in response to different 

levels of invasive cover. For example, as discussed earlier, the relationship between 

invasive cover and enhanced fire risk has not been quantified, so the change in fire risk 

could not be quantified. Such a lack of quantitative relationships between an 

environmental change and change in ecosystem service production level or quality, is 

common, even when harms have been documented. Therefore, knowing the prevalence 

of this problem, we relied upon ecological and economic first principles to create a 

theoretical relationship between change in vegetation and benefits. 

3.2 Change in Benefits with Treatment 

If bijk represents the realized benefits at site i with either treatment or natural 

recovery, we compare bijk with and without treatment to estimate the change in benefits 

for a particular management option. For each site, we consider the maximum possible 

benefits in the theoretical absence of invasive species4

, the percentage of native species 

realized after a management option is applied, Sik, and a fixed parameter, m, which is 

used to define a hyperbolic function of benefitsthat is specific to site, benefit and 

treatment. 

 

4

 We were not able to infer the value of all benefit metrics in the absence of invasives, however, we made 

the assumption of no invasives when data allowed. 
27 

Let bijk, with or without treatment, be represented by: 

 bijk = ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

j + ijk

ij ijk

m S

b S max

 (Eqn 4) 

We used this hyperbolic form for the benefits function (after Monod kinetics equation) 

because it had the desired form (continuously increasing function with decreasing slope, 

Figure 3) and because the parameter m had an intuitive interpretation. Parameter m

represented the percent native vegetation (value of Sik) at which half of maximum 

benefits were realized. Parameter m can be elicited from managers and researchers and 

adjusted for each benefit to alter the responsiveness of the benefits to changes in 

infestation level. In other words, the slope will vary as m varies. The parameter m was 

site-independent and benefit-specific, while max

ij b was site- and benefit-specific. 

The benefits equation had the property that at 100% native vegetation, full 

benefits were not achieved. It was useful to apply this equation for our purposes in order 

to reinforce the notion that we were evaluating success before full long-term benefits 

were realized (i.e., over a long time horizon). Therefore, we did not suggest that 100% 

native vegetation equated to full benefits early in the site recovery. Not until the plant 

community is mature (especially for shrubs), or until successive years pass without 

cheatgrass becoming the dominant species, would full benefits be realized. Therefore, as 

constructed here, the percentage of native vegetation, evaluated 2-3 years following 

treatment, represented a relatively early point in the restoration trajectory and was 

interpreted as a leading indicator of future long-term benefits. 
28 

0%

20%

40%

60%

80%

100%

0% 20% 40% 60% 80% 100%

% native vegetation on site

benefits (% bmax)

Figure 3. Benefits Equation Showing Responsiveness of Benefits to Parameter m and 

Percent Native Cover 

The parameter m is varied for each ecosystem service to change the slope of the function that 

relates level of infestation to benefits. See Equation 4. 

The functional forms used in benefit evaluation can be tailored to different 

services, depending on the information available to relate invasion to benefits. For this 

case study, the understanding of these relationships was tentative. Therefore, we did not 

diverge from this simple formulation for different services. Further work is needed to 

review empirical evidence and elicit best professional judgment on the nature and form of 

benefit response curves that more accurately reflect the causal relationships between 

treatment, biophysical effects, resulting changes in ecosystem services, and related 

benefits. 

3.2.1 Scaling Change in Benefits to Effects on Neighbors and Fire Size 

To derive the change in benefits, we calculated bijk with and without treatment and 

scaled the result by two factors: 

( )( ) 1 ( ) i i

without

ijk

with Δbijk = bijk − b + ΔC A (Eqn 5) 

where Ci, or the change in Ci, had a value between 0 and 1, and scaled the benefit 

function in proportion to the importance of the site for maintaining connections between 

native vegetation in the landscape surrounding the site. This factor is an indicator of the 

likely level of spillover benefits conferred on neighboring sites. The variable Ai scales 

the benefits with the size of the burned area. 

Forage Production 

Existence Values 

bmax

ij * %native 

 mj + %native 

m1 m2 

bij = 
29 

The Ci term reflected the importance of a given burned site for maintaining 

connections between uninfested areas. The change in Ci was calculated as the difference 

between the pre-fire connectedness of native vegetation and post-fire connectedness, 

assuming the burned site became dominated by invasive plant cover and acted as a “hole” 

in the mosaic of native vegetation (Figure 4). The change in landscape connectivity 

reflected the importance of the site for maintaining connections between native 

vegetation and therefore the importance of the site for preventing further decline of the 

neighboring sites. 

Ci was a proxy for the relative ability of site i to protect the stream of benefits 

derived from neighboring sites. The greater the loss of connection between native 

vegetation, the more site i acted as a “fire break” both in the literal sense and in the sense 

of potentially preventing degradation of services. The connectivity measures calculated 

using spatial data of native vegetation reflected both the proportion of the landscape in 

native vegetation and the spatial arrangement of that vegetation. Depending on the 

spatial arrangement of the native vegetation patches, cheatgrass seeds may have a greater 

ability to invade new areas, fire may have a greater tendency to spread, and organisms 

may have enhanced abilities to make use of the native vegetation. 

An individual patch of native vegetation differs in its ability to maintain 

connections (and thereby support services at neighboring sites) based on the 

configuration of surrounding land. For example, if the patch is an island of native 

vegetation surrounded by invasive species, the change in landscape-scale connectivity 

with invasion will be lower than a site that serves as a bridge between two patches of 

native vegetation across an area dominated by invasives. Therefore, we assume that the 

greater the change is in connectivity with the loss of the burned site, the greater the 

likelihood that services at neighboring sites will be disrupted. 

3.2.2 Scaling Benefits to Size of Treated Area 

The change in benefits was multiplied by area of the burn (in acres) to account for 

size when comparing benefits. A linear response of benefits with fire size is probably 

more acceptable for some services than others (e.g., forage vs. habitat). This topic is ripe 

for further research, but given the lack of demonstrated functional relationships between 

size and level of benefits for these particular services, we chose the simplest assumption. 

3.2.3 Spatial Pattern Metrics Used to Reflect Landscape Fragmentation 

The level of landscape fragmentation before or after a fire (Ci) can be calculated 

using many of the spatial pattern metrics developed to represent aspects of land cover 

fragmentation (O’Neill et al. 1988, Gufstafson 1998). These descriptive spatial statistics 

are used to evaluate the heterogeneity of landscapes and characteristics of land cover 

pattern through analysis of digital land cover maps. Land cover data are most commonly 

represented as a lattice of values or equivalent grid cells, as displayed in many types of 

imagery or Geographic Information Systems (GIS) system raster files. Typically, 
30 

contiguous patches of one or more habitat types are identified, delineated, and described 

through appropriate metrics, so that habitat qualities can be evaluated. 

A variety of techniques are used to calculate pattern metrics; some of which 

reflect information theoretic concepts such as the probability of encountering a given 

cover type adjacent to a site i within a landscape (McGarigal et al. 2002). Metric values 

are affected by data resolution, typical patch size within a given landscape, and by the 

classification system and other methods used to create the landscape data (Wickham et al. 

1997). Therefore, care must be taken to characterize the landscape in meaningful ways 

before applying such metrics. Of course, as is the case for all statistics, such metrics are 

only as good as the source data from which they are calculated. 

These metrics have been applied within numerous ecological and economic 

analyses in which fragmentation is of interest. For example, they have been applied in 

economic hedonic models to assess the effect of neighborhood characteristics on home 

values (Geoghegan et al. 1997). Landscape ecologists typically apply such metrics to 

evaluate aspects of habitat quality (Fahrig 2003, Villard et al. 1999) or to assess effects of 

human actions on biophysical condition (O’Neill et al. 1997, Jones et al. 2001, Hunsaker 

and Levine 1995). 

3.2.3.1 Calculating Change in Ci

We calculated fragmentation metrics for a standardized area or “window” 

surrounding each fire to evaluate the connectivity of the landscape. The size of the 

window was selected to be 10,000 hectares and was chosen to be smaller than the 

maximum patch size (contiguous area of native vegetation) and about twice as large as 

the largest fire size, in keeping with best practices for measuring effects in patchy data 

(Fortin and Dale 2005). 

In practice, no single metric can fully capture the aspects of risk to neighboring 

sites that we aimed to measure. We explored using several metrics ranging from the 

simple percent of area in uninvaded cover, to more complex metrics of patch shape and 

landscape fragmentation such as average perimeter to area ratio, largest patch index 

(LPI), and landscape characteristics such as contagion. Contagion is one of a class of 

metrics that measures interspersion and juxtaposition of land cover types. All metrics 

were calculated using FRAGSTATS software (McGarigal et al. 2002). 

Our final choice for Ci was based on finding a metric that responded predictably 

to fire size and that complemented other metrics used in benefit calculations. After 

evaluating metric results, we chose largest patch index (LPI) to scale neighborhood 

benefits. This metric had the advantage of an intuitive definition: patch index is the ratio 

of the area of largest patch to total landscape area, and thus is a measure of dominance of 

the native vegetation in the window surrounding each burned area. Also, this metric 

demonstrated a clear positive relationship with fire size (Figure 5) preventing this scaling 

variable from competing with fire size for effect on the landscape. 
31 

Although we avoided using a landscape metric that would compete with fire size, 

it could be said that we are skewing the importance of fire size by using two scaling 

measures that reflect size. However, the increase in LPI with increase in fire size is 

modest for all but the differences between the largest and smallest fires, so this was not a 

major concern. Alternatively, other metrics, such as contagion, can represent effects on 

the landscape connectivity but have less of a relationship to fire size. However, it is 

important to understand what the pattern metric is measuring to ensure the metric reflects 

the effect of interest. Many metrics are highly correlated and can substitute readily 

(Riitters et al. 1995) however, some can behave irregularly with environmental change, 

making interpretation difficult. 
32 

Figure 4a. Defining patches used in spatial pattern metrics 

The two boxes represent two schematics of vegetation maps with the pixels outlined. Native vegetation is 

shown as colored pixels and invasive vegetation as white pixels. All pixels that share a side or a corner 

are considered part of the same patch which is indicated by a common color in the map representation of 

native vegetation. When a pixel or a patch (group of pixels) changes from native to invasive plant cover, 

it can disconnect two patches that were previously part of the same patch. A fragmentation of the single 

native patch in the left side box occurs when the center pixel transitions to non-native vegetation (shown 

as a change from green to white). The two native vegetation patches in the right side box are now 

represented by two different colors indicating the two patches are now unconnected.

Figure 4b. Effect of Fire on Landscape Connectivity 

As with the top figure, these two maps of vegetation show native vegetation as colored areas and white 

areas as non-native invasive vegetation. Like colors indicate pixels are part of a connected patch of native 

vegetations, such as the large green patch that covers most of the left-hand box. The effect of the burn 

(white circle) is to create new unconnected areas of native vegetation shown as a change in color from 

green between the left and right boxes. This change indicates that, in the right box, an organism traveling 

in the green patch would no longer be able to reach the red patch without traversing at least one cell 

dominated by the invasive species. Mean contiguity declines between the left and right boxes (with the 

fire) indicating the reduced occurrence of adjacent cells containing native vegetation. Largest patch 

index, the ratio of the largest patch area to total area, also declines showing lower dominance of native 

vegetation in the landscape. 

Mean Contiguity = 0.666 

Largest Patch Index = 75.2 

Mean Contiguity = 0.576 

Largest Patch Index = 31.7 
33 

0

10

20

30

40

50

60

70

80

90

0 5000 10000 15000 20000

Fire Size (Acres)

LPI

Figure 5. Change in Largest Patch Index (LPI) with Fire Size for 46 Burned Areas in Idaho 

and Nevada 

The change in largest patch index represents the change in dominance of native vegetation after 

fire, assuming vegetation becomes dominated by cheatgrass. The change in LPI is correlated 

with fire size, one consideration in choosing this metric to represent fragmentation due to fire. 

3.2.4 Explicitly Measuring Invasion Risk to Neighbors 

Despite the inexact nature of Ci as an indicator of risk of loss of services from 

neighboring parcels, we considered it preferable to other available measures of invasion 

risk. It was beyond the scope of this project to develop our own model of invasion risk 

and thus we explored available models. While many models of invasion risk have been 

developed (Higgins et al. 1996), some for this specific region (M. Wisdom, pers. comm.), 

we did not find a model suitable for our purposes. In cases where managers have a more 

direct measure of risk of harm to neighboring areas, such a metric could be substituted. 

Our experience in searching for an ecological risk model demonstrates a typical 

problem of applying existing ecological research to economic analyses. We found a 

promising invasion risk model that had been developed for the Columbia River Basin 

(discussed in Wisdom et al. 2003) in which invasion risk by location was modeled as a 

function of several spatial variables. However, the model had some limitations for our 

purposes. Our initial concern was that risk of invasion was modeled exclusively as a 

function of biophysical variables and did not include any factors related to human 

activities. The second, and more important limitation, was that the model was developed 

and tested for a particular set of land use conditions and could not reflect the dynamics of 

seasonal fires. This was not a failing on the part of the researchers, rather it reflected a 

common impediment to successful risk analysis. The ideal of dynamic models using upto-date data is extraordinarily difficult to realize with current data collection and spatial 

modeling methods. Improvements can only be made if data are collected more 

consistently in time and space. 
34 

3.3 Measuring bmax - Maximum Potential Benefits of a Site 

The core of the benefit evaluation system was a framework of indicators 

constructed based on the economic concepts underlying production functions and 

location theory. (For further explanation see Wainger et al. 2001, Boyd and Wainger 

2002, Boyd and Wainger 2003). The indicators captured elements of the site and location 

that allowed a service to be produced (using a conceptual production function), and also 

reflected relative quality and location preferences of users. For example, a site may have 

the potential to serve as a recreational site, but if there is no access, the potential service 

cannot be realized. The indicators were used to measure the quality of the site for the 

intended use and evaluate whether complementary qualities were present to allow the 

service to be produced. Additional indicators were used to assess potential supply and 

demand of services produced at sites. 

The framework used to evaluate bmax incorporated a hierarchical set of indicators 

covering five aspects of value: 

• Site quality 

• Landscape quality 

• Site opportunity 

• Scarcity / substitutability 

• Risk of service disruption (service reliability) 

Site and landscape conditions were the primary factors responsible for basic service 

quality, but additional aspects of location (site opportunity) were envisioned to consider 

the complementary nature of adjacent lands (e.g., presence of campsites for recreation) 

and to weight the potential value of the services by proximity to users. 

Scarcity or substitutability of the service was another economic concept explored 

through the indicators. We assumed that, all else equal, greater scarcity and lack of 

substitutes increased the value of an ecosystem service. However, scarcity can only be 

effectively evaluated relative to demand, creating methodological challenges that we 

were not completely able to overcome due to constraints on data and analysis time. 

However, scarcity of services drove our selection of the services we evaluated. 

The risk of service disruption was assessed through indicators that examined risk 

of land conversion. Risk of land conversion was assumed to decrease relative service 

value since most benefits were derived from having the land in natural vegetation. The 

exception was the case of property protection benefits, which increased with the risk of 

land conversion to housing or business uses. 

Most valuation exercises incorporate the effect of income on willingness-to-pay 

for services. In this analysis, we ignored income effects because we were considering 

publicly owned land and taking a public land manager's perspective rather than a business 

or household perspective. Government decision-making does not typically embrace 

using income-related factors in resource allocation. 

Indicator choices for each service were devised based on a conceptual model of 

factors driving the quality of and demand for service at a particular location. As a result, 
35 

indicators selected to measure these qualities and the scale of analysis per service were 

usually distinct for each service. Indicators of service quality and accessibility, were 

developed to reflect preferences of stakeholders and were developed using existing 

economic theory and valuation studies. In addition, interviews with resource managers 

were used to develop other aspects of the production functions such as factors limiting 

service production and identifying the scarcest resources. 

3.3.1 From Conceptual Model to Indicators: Recreational Hunting Example 

Using the ecosystem service of recreational hunting support, we can illustrate in 

some detail how the indicators of site benefits were constructed by using literature 

sources to create conceptual models, and then how components of those models were 

used to create indicators of relative benefits. Our goal with both the conceptual model 

and the indicators chosen was to capture the potential change in recreational benefits to 

hunters with a change in site conditions. Within the environmental economics literature, 

changes in benefits are generally modeled as changes to consumer surplus associated 

with engaging in a particular activity before and after some environmental change (see 

Rosenberger and Loomis 2001 for review). Such models effectively generate a price that 

recreators are willing to pay to engage in an activity before and after an environmental 

change. Other models are used to evaluate the quantity of recreation demanded as a 

function of site characteristics. Often these two types of models are estimated within a 

single modeling framework. We explored both types of models to inform our conceptual 

model of site potential for providing recreational benefits. 

Our first goal in model development was to identify the pathway through which 

the invasion might change consumer surplus of hunters. In southern Idaho, cheatgrass 

impacts recreational hunting for pronghorn antelope by potentially 1) reducing the 

number of locations available for hunting, 2) reducing the size of the herd and 3) 

reducing the quality of the hunting experience. These effects can potentially increase 

costs to hunters through increased travel or other costs. Hunters might have to drive 

farther to avoid cheatgrass-infested sites, buy special gear to avoid problems with seeds 

getting embedded in socks and shoes, or incur costs from other adaptations. Or the 

presence of invasives might lower the perceived value or willingness to pay for a site, if 

the quality of that site decreases due to reduced bag rates and reduced opportunities to see 

wildlife. Extensive survey data has shown that hunters often care more about seeing 

game and the beauty of an area than killing game (Duda et al. 1995). 

Given these avenues for harm, models that accounted for effects on benefits from 

changes in travel costs, gear costs, bag rates, and aesthetics or ancillary wildlife viewing 

opportunities were of the most interest. We found a variety of relevant recreational 

hunting models or studies and supplemented those with additional outdoor recreational 

benefits models. Most importantly, the models had to provide us with a means to 

evaluate hunting participation rates or perceived quality based on site-specific 

characteristics that could be captured using available spatial data or that could be derived 

from spatial data through analysis. 
36 

Recreational demand in a region is a function both of the number of people 

participating and the intensity of their participation. Traditionally, recreational hunting 

participation rates have been well modeled as a function of demographic characteristics 

(e.g., income, age, gender, education level) and intensity of participation (total trips taken 

by participants) has been modeled as a function of costs, site quality, location 

characteristics and income or other characteristics (Phaneuf and Smith 2005). Models 

focused on assessing changes in site quality or changes in total economic benefits 

typically employ survey data showing how far people travel to participate, what 

substitute sites they considered, what they purchased, and the relative satisfaction derived 

from their visit (Bockstael et al. 1987, Bockstael et al. 1989, Loomis 1988). These multisite travel cost models are used to compare how much people valued a visit with how 

much they spent to participate. This information is then used to examine the values 

people hold for an environmental change in site condition. 

In addition to models developed from site-specific surveys, large survey databases 

are available to characterize recreation demand by region and activity. National or 

regional surveys of recreation participation can provide comprehensive information on 

participation rates, characteristics of participants, average trip distance and other 

information [National Survey on Recreation and the Environment (NSRE) 2000-2002, 

Cordell et al. 2005, National Survey of Fishing, Hunting and Wildlife-Associated 

Recreation, (USFWS 2001)]. However, site-specific surveys that contain more detailed 

information than national surveys are generally needed to develop site-specific benefit 

models. Although we obtained data on hunting area (large regions), we found the data 

inadequate for differentiating site quality and instead used costs of access and site quality 

to improve the spatial resolution of site demand characterization and to better understand 

the potential for sites to act as substitutes. 

Visitation databases or hunting permit records can also provide useful information 

about popularity of sites. High visitation indicates sites are popular, but not whether it is 

because of high quality, low-cost or both. Without further information, this is insufficient 

to understand how users will make substitutions between sites. 

Time cost of travel has been a component common to spatial allocation models of 

recreation trips and associated benefits of visitation, because of the information it 

conveys about level of demand and willingness to pay. It is understood that the more 

costly it is to access a recreation site, the lower the visitation, all else equal (e.g., 

McConnell and Strand 1981). However, if site quality is sufficient to offset higher travel 

costs, then sites with different costs may still produce the same level of consumer surplus. 

Since travel cost is also often the major site-specific expenditure (on a per trip basis) 

associated with outdoor activities such as hunting, travel time, by extension, it is a good 

measure of relative cost among sites. Travel time is the main location-specific variable 

responsible for travel costs since travel cost is typically modeled as proportional to time 

spent in travel. 
37 

3.3.1.1 Models of Trip Allocation 

Even with a good site-specific measure of cost of access, the aggregate behavior 

of how recreators distribute themselves among multiple recreational sites is difficult to 

capture in a simple model, and many alternative modeling strategies have been proposed. 

Difficulties arise from several factors including the complex spatial relationships between 

options such as substitution and complementarity effects. Substitution between sites is 

not well understood, but researchers have documented that availability of substitute sites 

in proximity to one another can, in some cases, reduce the number of trips to a given site, 

or, in other cases, increase trips taken to both sites. The latter, known as agglomeration 

effects, results from sites acting as complements (Kim and Fesenmaier 1990). 

Despite these complicating factors, researchers have attempted to model the 

spatial distribution, or allocation of recreational trips among sites, according to the 

variables that explain most of the response. One approach has been to use gravity models 

to demonstrate spatial relationships between population centers and alternative recreation 

sites (Freund and Wilson 1974, Sutherland 1982, McCollum et al. 1990, Isard 1972). 

These models are largely efforts to match observed patterns of aggregate trip distribution 

rather than attempts to model individual behavior. These models capture the effect of 

costs of access on site choice since they are based on the relative “pull” of sites given 

their distance from population centers of various sizes. 

Early gravity models were criticized for not controlling for site quality and 

generally failing to capture economic behavior of participants. However later models 

have attempted to address some of these concerns. McCollum, Peterson et al. (1990) 

applied a reverse gravity model in which they examined the number of trips to site j, as 

the joint probability of trips from potential origin sites i using data from a large 

recreational survey. A second linked model was used to estimate total trips generated 

based on user costs, site characteristics and market area characteristics. 

An allocation model, such as a typical gravity model, estimates how trips will be 

distributed among sites, given a fixed number of trips. However, total number of trips 

must also be evaluated by examining participation rates for given recreational activities. 

A major problem with all spatial allocation models is that they require observations of 

origin and destination of trips, which is typically collected through time-consuming sitebased surveys. Such information is needed to parameterize the gravity model or similar 

pattern-matching models. 

In our case study area, numerous alternative hunting sites are available since 

much of the publicly-owned land is open to hunting. Therefore, we sought a method that 

could be used to easily assess relative potential recreational demand at any particular site 

since scarcity did not seem to be an issue. We sought to develop a trip allocation model 

based on information known about average recreator behavior. 

If aggregate recreation demand at a site is typically modeled as: 

 E(x) = f(p, Q, y) (Eqn 6) 
38 

where E(x)is expected number of trips to a recreation site and: 

 p = travel costs

 Q = site-specific characteristics

 y = demographics of source population (income, education)

Then, we applied this model and our indicator framework described earlier, to generate a 

conceptual model of relative site demand for recreation that uses available data: 

 E(x) = f(p, q, r, s, u ) (Eqn 7) 

where: 

p = indicator of site opportunity, population-weighted travel time 

(number of people living within 1.5 hours travel time from site) 

q = indicator/index of site quality for hunting (quality for hunting and 

simultaneous activities such as bird viewing) 

r = indicator of availability of complementary features for hunting 

(e.g., availability of campsites) 

s = indicator of substitutability (presence of alternative sites of 

comparable quality within same travel distance) 

u = risk of site becoming undesirable for hunting within the next 30 

years (e.g., due to residential development) 

In our case, p represents the number of people with access to the site given that 

the majority of recreational hunting trips in this region occur within a 1.5 hour drive 

(based on travel distances documented in English et al. 1993). Travel time is closely 

related to travel costs but does not consider the cost of operating a vehicle or the 

opportunity cost of a recreator’s time. The population living within the 1.5-hour travel 

time (p) corresponded to the “site opportunity” class of indicator used in our indicator 

framework. Other variables represent site quality. We did not try to measure s since 

substitutes of equal quality appeared numerous, at least given our ability to distinguish 

site quality. 

We did not include information on demographics of the source population, even 

though these data would be available and such variables are standard for statistical 

models of participation (Bowker et al. 2006). Instead, because we did not expect major 

differences in demographic makeup across these areas, we simplified our framework by 

assuming that relative participation rates were constant across the case study area. In 

other words, if one in ten people engage in hunting in south Idaho in a typical year, we 

assumed that rate held for all populations equally and, therefore, reducing p by 90% 

everywhere would not change our measure of the relative demand for hunting at a given 

site. 

We present this model to show what drove our selection of indicators and to assist 

others who seek to find practical methods to measure benefits derived from natural 

systems. We note that despite our use of the expectation operator E(x) in equation 7, we 

did not fit this model in the same way that researchers with survey data fit a probabilistic 

model. Rather we used the elements of this model to create indicators that reflected the 
39 

relative number of expected number of trips and compared those values across sites. 

With our model, we were able to rate potential areas for their ability to be both highquality and low-cost sites, which would be sites that would tend to generate the highest 

consumer surplus, although we did not attempt to measure this directly. Our measures 

for site quality, landscape quality, site opportunity, scarcity and risk of service 

disruptions were captured through separate indicators and combined with indicators of 

potential demand to compare relative desirability of sites for hunting. Specific metrics 

used to evaluate these indicators and details of how they were combined into a single 

metric are described in the next section. 

3.4 Metrics Used to Measure bmax for all Services 

Similar to the recreational hunting example, conceptual models were developed 

for all four ecosystem services we considered and indicators were selected to measure 

relative demand for a service at a site. Indicators were selected for the characteristics of 

service quality previously described: site quality, landscape quality, site opportunity, 

scarcity and risk. The indicators selected are shown in Table 3 along with a positive or 

negative sign indicating whether they were deemed to be positively or negatively 

correlated with benefits. 
Table 3. Indicators Identified to Assess Relative Economic Benefits of Four Ecosystem Services 

Benefit Site Quality Landscape Quality Site Opportunity Scarcity 

Recreational Hunting (pronghorn antelope) 

Sage-grouse habitat quality (high, medium, low) (+) (proxy for % cover of native vegetation, etc.) 

Camping availability (developed or backcountry campsites) (+)

Population within 1.5 hours (+) 

Alternative sites of same quality within same travel distance (-) 

Forage Production 

Animal Unit Months (AUMs)/hectare (+) 

Distance to markets (-) Availability of water sources (+)

Existence Values for characteristic species, sage-grouse 

Sage-grouse habitat quality (high, medium, low) (+) 

Local level of fragmentation (spatial pattern metric) (-) 

Regional connection to habitat patches (spatial pattern metric) (+) 

Probability of population falling below minimum viable population size (locally or regionally) (-) 

Property Protection Population within 3 mile radius (+) Within or adjacent to major urban area (+) 

Sign following metric indicates whether correlation with benefits is positive or negative. Grey text indicates indicator was 

data or because of correlation with another variable. See text for further explanation. 
41 

3.4.1 Site Quality 

For each service, an indicator of site quality was developed to reflect the quality 

of the service derived from on-site characteristics such as level of natural function. 

3.4.1.1 Existence Values for Sage-Grouse 

A composite measure of quality of habitat for Greater sage-grouse (Centrocercus 

urophasianus) had previously been developed by the Bureau of Land Management and 

was adapted for our purposes. BLM, using expert judgment, divided sage-grouse habitat 

into four classes that identified habitat importance and restoration potential. We 

eliminated the class that showed potential for habitat restoration because it had limited 

extent and the parameters for defining restoration potential were not available. We 

ordered the remaining classes on habitat quality into high (best in original data), medium 

(good in original data) and low (moderate in original data) quality (Figure 6). Areas 

outside these defined areas were not considered to be habitat. Burned areas were 

evaluated by examining the site quality class at the location of the fire. 

Figure 6. Habitat Quality for Sage-Grouse

Source data from ICBEMP 2004. 

3.4.1.2 Hunting Quality for Pronghorn Antelope 

Site quality for pronghorn antelope (Antilocapra americana) hunting was judged 

based on the suitability of the site for another indicator species, sage-grouse. Since both 
42 

species are dependent on sagebrush, and because hunters prefer areas where they would 

have an opportunity to simultaneously engage in viewing native species (Duda et al. 

1995), this was the best available marker of quality of hunting experience given that we 

did not have data on antelope habitat directly. Scores for this indicator were thus the 

same as scores for the existence values for sage-grouse. 

3.4.1.3 Forage Production 

Site quality for production of animal forage for ranching was characterized using 

animal unit months (AUMs) per hectare on grazing allotments (Figure 7). GIS data 

showing allotment boundaries and accompanying data on characteristics of active grazing 

allotments were obtained from the Idaho State Offices of the U.S. Bureau of Land 

Management (BLM). Other site quality factors were considered, such as availability or 

quality of water supply and suitability for feed crop production, however data could not 

be found to characterize these factors. This measure of potential yield could readily be 

turned into a value of production using price of commodities and other variables, 

however, information on types of animals being raised was not available by allotment 

within the database, although such data may have been available elsewhere. Also, if we 

assumed the most common type of cattle was raised at all sites, the values would not vary 

over the study region, and therefore would not change our measure of relative value 

among sites. 

3.4.1.4 Property Protection 

For property protection, the indicator of site quality was the number of people 

living within a 3-mile radius of the burned area. The assumption was that the greater the 

number of people within this area, the more structures at risk and the more people would 

potentially benefit by treatments to reduce fire risk. Data on property value or presence 

of vulnerable infrastructure could be used to enhance this metric, but data were not 

readily available for the entire region. Values for nearby residential population were 

normalized to a 0-100 scale with 100 being the highest number of people in the vicinity. 
43 

Figure 7. Map of Forage Production Quality Indicator: Animal Unit Months per Hectare 

Source data courtesy of BLM. 

3.4.2 Landscape Quality 

Landscape quality captures elements of landscape configuration that complement 

site quality in order to enhance the overall service quality. These indicators describe 

conditions of the surrounding landscape that allow sites to produce quality services if onsite conditions are also good. For example, a site might have high quality native 

vegetation but be isolated from surrounding habitat by urban development. Such site 

context would prevent the site from realizing its potential for habitat for a sensitive 

species. Landscape quality indicators were developed for the services of recreational 

antelope hunting and existence values for sage-grouse. Landscape indicators were 

combined with the site indicators for these two categories to create an overall quality 

metric for each service. Scores for all services were adjusted so that the total number of 

indicators used did not affect total scores. 

3.4.2.1 Recreational Antelope Hunting 

The number of people within 1.5 hours (~75 miles) of the site was the landscape 

quality indicator developed for recreational antelope hunting. The distance that 

recreators travel was constrained by using the upper bound discussed in English et al. 

(1993, Table 11) that 75% of hunting trips in the Rocky Mountain region, which contains 

Idaho, took place within 75 miles of the originating site. This estimate was somewhat 

lower than some other travel distances that had been estimated by other researchers. For 
44 

fishing, one study suggested sites within a 4.5 hour drive are reasonable substitutes 

(Whitehead and Haab 2000, for the southeast US). At 40 mph average trip speed, 4.5 

hours translates to approximately 180 miles. Other studies used 100 miles from home as 

the relevant trip distance (Feather and Hellerstein 1997), although they acknowledged 

that different activities have different scales. 

3.4.2.2 Existence Values for Characteristic Species 

Sage-grouse are dependent upon contiguous tracts of sagebrush for habitat and 

recent studies suggest this species is particularly sensitive to human disturbance and 

avoids developed areas and roads (Naugle et al. 2006). Therefore, to develop a landscape 

quality indicator that reflected this component of their habitat requirement, we considered 

several landscape pattern metrics designed to examine habitat fragmentation. In contrast 

to the spatial pattern metric used to evaluate the effect of restoration on neighboring 

pixels (Section 3.4.2), this metric was developed as a specific landscape habitat quality 

measure affecting sage-grouse. These spatial habitat metrics are commonly used to 

examine whether patches of potential habitat form migration corridors or provide 

sufficient undisturbed area to provide high quality habitat, given the specific life cycle 

requirements of a species. 

Because sage-grouse avoid sagebrush adjacent to disturbed areas, the total core 

area metric, calculated for the landscape scale, was chosen to reflect landscape habitat 

quality. Core area is a metric that refers to the area within a patch that is greater than a 

specified distance from the patch perimeter. The metric was calculated for a window 

around each fire site pre- and post-fire (assuming full conversion to cheatgrass) to 

examine the potential maximum effect of fire on total core area available to sage grouse. 

This landscape quality indicator was calculated using several GIS processes, 

which were automated in Python and the core area metric was calculated using 

FRAGSTATS (McGarigal et al. 2002). Because the sage-grouse responds to 

fragmentation over short distances, we sought fine resolution data to evaluate this aspect 

of fragmentation. Relatively fine scale (30 meter cell size) vegetation data with detailed 

vegetation categories were obtained from the USGS GAP analysis for Idaho (Scott et al. 

2002). All vegetation types containing sagebrush were considered as potential sagegrouse habitat. A 10,000m by 10,000m (10,000 ha) window surrounding each fire was 

evaluated for each site and a buffer of 30 meters (one cell) was used around patch edges 

to define non-core area. The metric is returned as a value between 0 and 100 that 

measures the percentage of the landscape in core area. 

To develop a single metric of habitat quality for sage-grouse that incorporated site 

and landscape characteristics, we combined the habitat site quality developed by BLM 

with the landscape quality indicator of % of habitat core area surrounding each site. The 

core area indicator (scored between 0 and 100) was multiplied by a site quality factor 

based on the habitat quality (high, medium or low) developed by managers. The highest 

quality site value was assigned a scaling factor of 1, medium quality used a scaling factor 

of 0.75, and low quality a factor of 0.5. Therefore, the highest indicator values occurred 
45 

where the landscape in the vicinity of the site showed the highest percentage of core area 

and where managers had assigned high potential habitat value based on multiple site and 

landscape characteristics. 

It could be said that the site quality developed by managers would reasonably 

include fragmentation, given the sensitivity of the species to this aspect of habitat. The 

experts who drew the general boundaries of best, good, and moderate quality habitat sites 

undoubtedly considered this component of the landscape. However, the generalized 

boundaries they created were not intended for comparing sites at a fine scale. Therefore, 

somewhat counter-intuitively, our landscape scale indicator provides more detailed sitespecific information to judge relative habitat quality than our site quality indicator. 

Site-specific quality indicators can be among the most difficult to find in a GIS 

format when conducting regional screening. Typically, coarse scale data are used to 

suggest site quality when conducting regional screening. However, such data cannot 

capture site-specific conditions that can limit site quality such as fences or concentrated 

disturbances such as toxic waste sites or legacies from historic land use. Nonetheless, it 

is widely recognized that landscape context can serve as a strong indicator of site quality 

(Brooks et al. 2006), especially in the absence of specific limitations that are undetectable 

at coarse scales. 

3.4.3 Site Opportunity 

3.4.3.1 Recreational Antelope Hunting 

As previously discussed, we evaluated the portion of the population living within 

a 1.5 hour drive of sites as the site opportunity indicator for hunting. We initially 

evaluated two techniques to estimate the population able to reach potential recreation 

destinations. In one technique a distance-decay function was estimated using a kernel 

density estimator. This function was used to probabilistically distribute population from 

multiple population centers assuming equal travel speed in all directions in the landscape. 

In the other technique, a travel-time model was developed using the road network and 

applicable road speeds. Both techniques are available within the GIS software package, 

and are readily available for managers to use. Each offers advantages in terms of 

evaluating potential patterns of travel, however the travel time model was eventually used 

in comparing benefits because of the greater realism in estimating travel times and thus 

costs. The major limitation to this technique is that it cannot easily distribute population 

from multiple population centers to a destination site. We describe the techniques for 

both methods in the interests of informing choices by managers. 

Estimating Relative Accessibility Using Kernel Density Estimation 

The purpose of kernel density estimation is to interpolate an underlying density 

curve given a set of observed data. In constructing this estimate, a curve is fit to each 

observed data point. The function of the fitted curve, which must integrate to 1, is called 

the kernel function. The density estimate is not overly sensitive to the kernel function 

and the most commonly used kernel function is the normal or Gaussian function due to 
46 

its mathematical simplicity. The sum of these fitted curves produces the kernel density 

estimate and yields the following equation: 

 ∑=

− =

n

i

i

h

x x

w

nh

f x

1

( ) 1 ( ) (Eqn 8) 

where xi is the observed data point (for i = 1,2,...,n), w(.) is the kernel function, h is an 

arbitrary parameter known as the bandwidth, and the term (1/nh) is a normalizing 

constant to make certain the probability function integrates to 1. 

 The process of this estimation has been automated through a built-in function in 

ArcGIS. This function fits a smooth surface to each observed data point where the 

surface value is greatest at a peak over the data point and decreases with distance from 

the observed point (Figure 8a). The kernel function used to fit the surfaces to multiple 

points on the landscape is a quadratic function commonly used in three-dimensional 

density estimation. A radius is then specified to determine the area over which the 

density will be estimated. Since each data point has a unique surface and these surfaces 

overlap, the values of the surfaces within a certain raster cell must be summed, and the 

sum is the density estimation at that raster cell. 

Using this kernel density estimator in ArcGIS, density of trip potential was 

predicted (as seen in Figure 8a). For each raster cell in this figure, the result is an 

estimation of the number of people who would likely travel to this area. For this 

estimation, the observed data used was population, and the radius of maximum trip length 

was 75 miles (English et al. 1993, Table 11). When combined with other indicators of 

service quality (Figure 8b), such trip density measures can be used to examine 

substitutable areas (Figure 8c) and areas offering the highest probability of providing 

continued future service (Figure 8d). 

The kernel density estimator allows for a density distribution of trips, with more 

trips occurring close to population centers and fewer occurring far from population 

centers. However, the assumption of uniform travel costs in all directions is unrealistic 

except for limited circumstances. 
Figure 8a. Potential Trip Density

Map showing result of fitting a probability density (distance-decay) function to population centers. 

Figure 8c. Substitutable SitesZone of potential substitutes is developed using sites within the highest trip density zone that co-occur with areas of high quality habitat. 

Figure 8b. Habitat Quality over Trip DensiMap of sagebrush communities (proxy for hadensity zones from Figure 8a. Figure 8d. Lowest-Risk - Highest Benefit SMap shows roads (in red), a factor in risk of lon Figure 8c. Blue boxes outline sites with hprobability of providing service streams in thwere those far from roads and within unfragmindicating highest quality habitat, assuming a
48 

Travel Cost Model of Recreation Accessibility 

The travel cost model uses the road network to more realistically evaluate site 

accessibility, although it does not provide the ability to distribute population according to 

a density distribution. The 75-mile travel radius used in the kernel density function was 

translated into 1.5 hours travel time and it was assumed that the number of recreational 

trips would be a constant proportion of available population. All of the fire sites were on 

public lands and were therefore accessible for hunting. 

The number of people within 1.5 hours of the site was determined for each fire 

site through a series of GIS analyses (Figure 9). First, a “cost surface” map was created 

for the region using a combination of road and slope data (see Section 4.3.1.2). In this 

cost surface, each 1,000m by 1,000m raster cell was assigned a value that corresponded 

to the amount of time it would take to cross that cell. This time was determined by 

assigning speed limits by road class, or, in areas without roads, assigning a speed based 

on slope class (e.g., slope <10%, slope 11-30%, slope >31%). A raster file representing 

population was created using US Census data and assigning population to each grid cell 

based on the population density of the corresponding census block group. Using a series 

of GIS analyses (ESRI ArcGIS Desktop v. 8.3 software automated in a Python script) the 

number of people living within a 1.5 hour radius were summed for each fire. Values 

were scaled to a 0-100 scale, with 100 being the maximum people observed living within 

a 1.5 hour radius. 

3.4.3.2 Existence Values for Characteristic Species 

Conceptually, we identified the need for a variable of site opportunity for sage 

grouse habitat quality that represented the spatial connection between a population at a 

particular site and the broad-scale habitat mosaic within the Intermountain West. Such a 

metric would represent the importance of any given site relative to alternative habitat that 

the species might use. Such metrics are particularly important for migratory species that 

need stopover sites to be located within a day’s flying distance of one another in order to 

maintain a migratory pathway. Similarly, a habitat mosaic may provide insurance that if 

a local population dies out, it remains connected to a source of new recruits. However, in 

practice, when we identified the particular habitat needs of the sage-grouse we did not 

feel such a metric could be supported with available data and understanding. 
49 

Figure 9. Area Accessible within 1.5 Hours Travel Time of Burned Area 

Burned area is represented as a black dot. 

3.4.4 Scarcity and Substitutability Indicators 

Our main aim with the scarcity metrics was to demonstrate the availability of 

substitute sites to the user population of any particular service. 

3.4.4.1 Recreational Antelope Hunting 

We envisioned scarcity indicators for use services such as recreational hunting 

that could demonstrate the scarcity of sites for particular services and how people would 

be likely to make trade-offs among sites. For example, we expected to compare the 

number of equivalent recreational sites available to a given population and rank the 

scarcity of particular sites in terms of availability. Our decision to use the cost-distance 

model for assessing travel time for recreation services limited our ability to easily 

evaluate substitutability of sites among many populations. However, we demonstrated 

our intended methodology for assessing substitutability with the kernel density estimator 

(Figure 8c). 

In addition to methodological challenges, such scarcity/substitutability indicators 

turned out to be difficult to capture for these services in this landscape context, primarily 

because of the abundance of substitutes for most services. The abundance of lands open 

to hunting in this region dramatically reduced the need for such indicators. However, 

antelope hunting opportunities appeared to be in decline with advancing cheatgrass. 

More spatially refined data on favorite hunting locations would be needed to better model 

how hunters make substitution decisions between sites and therefore, where local scarcity 

for services might be present. 
50 

3.4.4.2 Existence Values for Characteristic Species 

Of interest for evaluating the value of sites for providing existence services is 

whether a species is maintaining a sustainable and resilient population. For the sagegrouse, the population does not appear to be endangered across its entire habitat since 

legal petitions to list the species as threatened or endangered were rejected in 1995 

(USFWS 1995). At that time, the US Fish and Wildlife Service found that a large 

population remained, although it was in modest decline when evaluated over its entire 

range. In some areas, the population appeared to be stable or increasing. 

For services that depend on maintaining a particular species or ecosystem, 

managers have several types of analyses they may consider to evaluate if the population 

is viable over the long term. “Population viability analysis” is an umbrella term for 

several techniques aimed at determining whether a site is sufficient to maintain a 

successful breeding population that is also resilient to disease or other perturbation 

(Coulsen et al. 2001). Such analyses will provide indicators of risk that the population 

cannot be maintained on a given site. 

We explored several indicators for habitat scarcity of sage-grouse and hunted 

species (antelope and deer) including irreplaceability (Lawler et al. 2003, Ferrier et al. 

2000), critical habitat areas (e.g., overwintering habitat), and scarcity of regional habitat. 

Managers had identified deer overwintering habitat as a resource that was potentially 

becoming scarce since these low elevation areas are most affected by cheatgrass. 

However, we did not include this component since our existence service was narrowly 

defined for sage-grouse. Other metrics were rejected due to lack of appropriate data. 

3.4.5 Risk Indicator 

The risk indicators were intended to reflect risk of service loss that was beyond 

the control of the rehabilitation project. Just as people decide not to fix an expensive 

component of a broken car when too many other things are likely to break soon, 

managers may decide not to rehabilitate a site that has a high likelihood of losing the 

ability to produce a service due to human activities (e.g., land conversion) or natural 

processes (e.g., ongoing plant succession). Managers may also consider the risk that a 

service will lose value in the future, such as waning popularity of hunting a particular 

species. 

3.4.5.1 Residential Development Risk 

For all ecosystem services, we used the same risk metric to capture risk of land 

conversion to residential use. In southern Idaho, land managers identified the greatest 

threat to habitat, other than invasive plant species and fire, as being the risk of conversion 

to residential development. We searched for existing research on residential land 

conversion risk for the area by calling government land use planning agencies and 

conducting web searches. We have previously been able to find assessments of future 

land development risk from land use or infrastructure planning agencies at the local or 

state level. However, in this case, we did not find any government research, nor did we 
51 

find any academic models of conversion risk for this region. Digital zoning maps were 

also not readily available, although we were able to obtain maps of land ownership from 

the US Forest Service (ICBEMP 2004). 

A variety of models are available to estimate risk of land conversion (see reviews 

by Irwin and Geoghegan 2001, Parker et al. 2003) although most require time-consuming 

data development and statistical analysis. The extraordinarily high percentage of 

government-owned land and the rural nature of the case study setting limited the 

applicability of most land use change models. 

An in-depth analysis of conversion risk was beyond the scope of this project, so 

we developed an indicator to serve as a place-holder for our case study demonstration. 

We selected three metrics that are common to land use change models: travel distance to 

a main city in the district, proximity to major roads, and existing low density residential 

use. Using distance to a central business district is a common determinant of a 

component of risk of land conversion (e.g., Bockstael 1996, Landis 1995) and existing 

density and roads are typically used in pattern-matching type models of land conversion 

(Theobald 2005, Verburg 2006, Parker et al. 2003). 

Such pattern-matching approaches use historical land conversions and presence of 

major predictors such as roads to demonstrate the spatial “contagion” common among 

subsequent land conversions. We excluded publicly-owned land from consideration 

thereby eliminating all categories of protected land from possibility of conversion to 

developed uses. Such an ad-hoc system of indicators can only provide a rough indication 

of conversion risk given the many factors that affect attractiveness for development. 

Managers who do not have access to carefully developed predictions of conversion risk 

may choose to ignore this factor or substitute professional judgment of realtors or land 

use planning professionals. 

To generate the risk indicator for conversion of agricultural or natural land to 

residential or commercial uses, we developed three metrics for private lands within the 

Twin Falls BLM district. Government-managed lands were excluded from the analysis 

of development risk and not given any indicator scores. The first risk metric was travel 

time to the city of Twin Falls, which was used to reflect access to the principal business 

district. The areas closest to Twin Falls were given the highest risk classification. 

Distance to primary roads was the second metric developed. Primary roads included 

Interstates, US highways and state highways (with or without limited access). We used 

the log of distance to primary roads to represent the enhanced risk for parcels in close 

proximity to roads. 

The third metric used was risk of development due to proximity to low-density 

housing. This indicator was measured by examining a map of land use developed to 

identify wildland urban interface (WUI) areas. The map contains 14 land cover classes 

describing combinations of level of residential development and vegetative cover, of 

which we designated three low density housing cover classes as the areas of interest for 

new development. A 3x3 cell neighborhood around each 30-meter cell was examined, 

using a moving window within the GIS, for presence of these low density housing land 
52 

classes. Risk was assigned to a cell in a binary fashion with high risk given to sites that 

had presence of low density housing and no risk given to sites without low density 

housing in the window. 

The three risk factors were combined by adding the three metrics, whose scores 

had all been assigned based on a 0-3 scale, with 3 being the highest risk. The final risk 

raster contained values ranging from 2 to 9, which were then used to adjust other benefit 

indicators, as described below. Because government lands were excluded, the majority 

of sites were not ranked for development risk and were effectively given no risk of 

development. 

3.4.6 Combining Indicators into a Single Metric of Benefits 

We were able to simplify the difficult issue of how to combine indicators for each 

service into a single benefit index by limiting the number of indicators used. Indicators 

were kept to minimum by carefully selecting only the most representative metric for each 

of the five indicator categories (Table 3). Based on our interpretation of the literature, 

interviews with managers and best professional judgment, indicators were developed that 

1) represented the variable that would explain the majority of the variability among sites 

and 2) was represented in existing datasets. 

Data and analysis complexity concerns also served to limit the number of 

indicator categories calculated and scarcity indicators were deemed largely unnecessary 

given the relatively high number of substitute sites for our selected services in the nearterm. For the services of Forage Production and Property Protection, only a single 

quality indicator was developed creating the need to combine two indicators for site 

quality and risk. The services of Recreational Hunting and Existence Values were 

evaluated with three indicators (site quality, landscape quality/site opportunity and risk) 

that needed to be combined. 

The technique used to combine indicators was to scale all continuous variables 

between 0 and 100% and multiply indicator values together. Essentially, we treated 

indicator scores as probabilities of achieving the highest possible service benefit and 

combined them as we would any probabilities. This crude method of developing the 

“production function” for service benefits was a necessary construct to fully demonstrate 

the analysis, although we do not deny that the objective information available to create 

such production functions is limited. We used our own best professional judgment based 

on literature review and interviews with managers, however our decisions were meant to 

serve as placeholders for a more open process that we envisioned would involve expert 

elicitation using groups of local experts. 

Not all indicator variables were initially measured as continuous variables and 

therefore additional methods were applied to create comparable scores from the ordinal 

values used for sage-grouse habitat quality and urban development risk. For the sagegrouse habitat indicator, values between 0 and 100 % were assigned to each of the three 

levels of habitat quality (high, medium, low) for each of the two services being evaluated, 

Recreational Antelope Hunting and Existence Values for Sage-Grouse (Table 4). The 

values were developed based on our team’s best professional judgment (developed from a 
53 

literature review and manager interviews) of how a level of site quality would affect the 

benefits derived from that service. 

When these site factor scores were multiplied by the indicator scores for 

Landscape Quality or Site Opportunity, they either acted to maintain high scores when 

the best conditions co-occurred or they became downward adjustments when lower 

quality conditions occurred on a site. The downward adjustments were more substantial 

for recreational hunting than for sage grouse habitat because hunters were considered to 

be more sensitive to degraded habitat because of their ability to move between sites and 

thereby easily find substitute high quality sites rather than accepting lower quality sites. 

Table 4. Site Quality Factors Used when Combining Service Benefit Indicators 

Recreational Hunting Existence Values 

for Sage-Grouse 

Sage-Grouse Habitat 

Quality 

Continuous Site 

Quality Score 

Continuous Site 

Quality Score 

High 100% 100% 

Medium 75% 90% 

Low 50% 80% 

Not sage-grouse habitat 0% 0% 

The Risk of Service Disruption indicator was interpreted as a probability of 

service persistence into the future. Higher risk of new land conversion was used to 

reduce potential service benefits for services related to hunting, forage production and 

existence values. For all services except property protection, benefit indicator scores 

were decreased by a maximum of 25% (risk indicator value = 75%) for the highest risk 

category of 9 and were not adjusted for the lowest risk scores of 2 (risk indicator value = 

100%). Values in between 2 and 9 were scaled proportionally, so, for example, a risk 

score of 6 resulted in a benefit score reduction of about 15% and a risk score of 3 resulted 

in a benefit indicator reduction of about 4%. Risk-adjusted scores are shown in Table 5. 
54 

Table 5. Benefit Indicator Scores for Selected Sites 

(normalized values of 0-100%) 

Site Quality Landscape

Quality 

Site 

Opportunity

Risk 

(Urban 

Development)

Risk Adjusted Benefits 

Site 

ID 

Existence 

Values 

Recreational 

Hunting 

Forage 

Production 

Property 

Protection 

Existence 

Values 

(Sage-grouse)

Recreational 

Hunting 

Recreational 

Hunting 

Existence 

Values 

(Sagegrouse) 

Recreational 

Hunting 

Forage 

Production

Property 

Protection*

52 100 100 18.3 1.0 56.1 29.7 100 56.1 29.7 18.3 1.0 

53 90 75 23.5 0.5 37.4 82.4 100 33.7 61.8 23.5 0.5 

55 0 0 0.00 2.3 3.8 35.8 92.8 0.0 0.0 0.0 2.3 

56 100 100 22.9 1.0 64.6 33.8 100 64.6 33.8 22.9 1.0 

58 90 75 0.0 0.1 38.3 0.0 100 34.4 0.0 0.0 0.1 

59 90 75 34.9 0.2 62.6 37.9 100 56.3 28.4 34.9 0.2 

60 80 50 35.9 0.5 68.9 46.6 100 55.1 23.3 35.9 0.6 

61 90 75 13.9 0.1 46.9 32.3 100 42.2 24.2 13.9 0.1 

63 80 50 36.5 1.5 4.9 30.8 100 4.0 15.4 36.5 1.5 

66 90 75 69.2 0.1 40.2 0.0 100 36.2 0.0 69.2 0.1 

67 90 75 0.1 0.1 57.5 25.8 100 51.8 19.4 0.1 0.1 

69 100 100 35.9 0.4 62.0 38.1 100 62.0 38.1 35.9 0.4 

81 100 100 24.2 0.1 60.3 23.7 100 60.3 23.7 24.2 0.1 

* Property Protection values were highly skewed so that even though values range from 0-100 over all 

sites, scores shownare quite low. 
55 

3.5 Benefit Measurement Discussion 

Our attempts to quantify the net benefits of treatment met with many roadblocks 

largely due to limitations on the quantitative evidence for cheatgrass impacts on 

ecosystem service benefits. However, much qualitative and descriptive information was 

available and we were able to apply data, information and best professional judgment to 

create a system to capture expected effects of treatment using indicators of ecosystem 

service benefits. The system we developed relied on applying basic ecological or 

economic functional relationships, yet, demonstrated the methods one might use to 

characterize site and location characteristics that contribute to location-specific service 

value. We showed that aspects of future site benefits could be captured within a static 

analysis and that appropriate information was available to characterize a wide array of 

ecosystem services. With the rest of this report, we develop complementary information 

on costs and probability of effective treatment so that this information on relative benefits 

can be used in making prioritization decisions using cost-effectiveness analysis or an 

optimization model that maximizes change in benefits for a budget constraint. 

4. Evaluation of Treatment Costs 

4.1 Facility Location – Application of Location Theory 

For purposes of estimating costs of enhancing ecosystem services at sites, we 

characterized potential treatment sites as “factories” of ecosystem services and our 

investment decisions were then analogous to facility-siting problems. For facility-siting 

problems, locations are chosen that will minimize costs of production and delivery of 

goods and services (Brandeau and Chiu 1989). Locations may also be chosen to 

minimize losses from competing producers or to take advantage of agglomeration effects. 

In our analysis of the costs and outcomes of prevention strategies, we similarly sought to 

evaluate the costs of production (treatment) and benefits of final products (ecosystem 

services) at specific locations. 

The issue of maximizing returns through facility location choice is a well-studied 

concept in economics. Alfred Weber (1909) is generally acknowledged as having 

formally introduced location theory by examining the problem of siting a warehouse to 

minimize travel distance between the warehouse and customers, although he was not the 

first to consider spatial pattern of economic activity. Weber’s work was expanded upon 

by many, including groundbreaking work by Walter Isard, who examined facility 

location, optimal land use, routing problems, and other location-dependent questions (see 

Brandeau and Chiu 1989 for review and Isard et al. 1972). Advances in computing 

allowed sophisticated network analysis to be used to determine travel times and find 

efficient routing solutions (Jensen and Bard 2003). Some recent applications of facility 

location have included siting bio-energy facilities to minimize costs of inputs (Noon et al. 

2001). 

To understand the potential net benefits of enhancing ecosystem services by 

treating invasive species, the costs and benefits specific to that site must be examined. 

Our location-based approach to estimating costs departs from previous analyses of 
56 

invasive treatment that assume costs are a constant per acre value (e.g., Denne 1998, 

Zavaleta 2000). Since site accessibility to labor and equipment affects cost of treating at 

a particular location, we evaluated the costs by considering treatment “delivery” times to 

location i. Economies of scale were important to capture because it is well-established 

that treating small areas is generally more costly per acre than treating large areas (Mills 

and Bratten 1988, Hesseln et al. 2004). However, it has been suggested that treating 

small outlier populations of invasive plants is the best strategy for long-term control of 

invasives plants (Moody and Mack 1988). Therefore, it was important to understand the 

relative costs and risk-adjusted benefits of small vs. large and remote vs. near sites. 

We took an approach to estimating costs that considered site and location factors 

for two reasons. First, the effect of location on treatment cost increases when repeated 

trips to the site are needed, as is the case for most invasive species treatments. In the case 

of small treatment areas, travel costs can represent a large fraction of treatment costs 

(Mills and Bratten 1988). Second, we wanted to be able to compare the marginal costs 

and benefits of treating different size areas in order to find an efficient size of area to treat 

in each location. Locally heterogeneous conditions may dramatically affect the 

relationship between average cost and size of area treated. Therefore, a constant per acre 

cost may not capture important heterogeneity of costs with location or allow the 

relationship between size of area treated and net benefits to be explicitly examined. 

The need for such site-specific factors in cost estimation can be weighed against 

the increased time required to make such estimates. In deciding on treatment options, 

managers must choose both which sites to treat and how intensively to treat each site. 

Keeping cost estimation systems simple is important because decision-makers typically 

need to screen many areas to evaluate the best use of resources. Yet, spatial analysis 

tools and available spatial datasets are making such spatially-detailed estimates 

increasingly quick and easy. Where good data exist, use of spatial analysis within 

Geographic Information Systems (GIS) allows a wide variety of location factors to be 

considered simultaneously, although some factors may still need to be assessed through 

site visits. By using such tools to create maps of costs and cost factors, managers can 

readily compare trade-offs between treatment locations. 

4.2 Cost Model Framework 

To evaluate costs by location, we created a spatial cost model and evaluated data 

available to parameterize the model. We developed the model with the general case in 

mind of cost estimation for any type of invasive species treatment decision and 

eventually parameterized a simplified model based on the specific treatments used for 

burned area rehabilitation programs in the case study area. The costs of treating a site 

were conceptualized as a function of fixed and variable costs with variable costs made up 

of travel time, search time and treatment time. These categories incorporated costs 

related to equipment, materials, personnel and transportation. 

The cost of treating a single cell at location i on the landscape with a treatment 

intensity k (PCik) was characterized in terms of the following variables: 
57 

 TCik = FCk + JCk*JTi + SCk*STi + CAik*Ai +DCk*D (Eqn 9) 

FCk = Fixed Costs for treatment intensity k

JCk = Journey (Travel) Cost, or the hourly cost of transporting all personnel and 

machinery for treatment k from the origin cell to treatment destination i

JTi = Journey Time (hours) to site i is a function of road networks, streams and 

slopes 

SCk = Search Cost, hourly cost of searching for area to treat for treatment k, 

which is a function of treatment method 

STi = Search Time (hours) is a function of site characteristics 

CAik = Treatment Cost per area, cost of treating location i with treatment k

Ai = Area treated (acres) 

DCk = Daily Costs, added costs beyond the hourly rate incurred for each 

overnight stay (e.g., overtime pay, hotel and meal costs, etc.) 

D = Number of overnight stays 

i = Site location 

k = Treatment phase 

To simplify calculations of treatments that involving multiple trips, we measured costs of 

all trips to complete treatment regime k. Therefore, journey costs and treatment costs for 

k could reflect multiple trips. 

We were able to simplify calculations of fixed costs because much of the 

treatment work was contracted out by the federal agencies that manage the land. 

Therefore, costs could reasonably be estimated by focusing on the short-term costs of 

treatment and assuming that management and facilities costs were fixed. However, we 

included agency personnel costs to plan, oversee and monitor treatment in this model. 

Overhead costs were ignored because they were generally a fixed percentage of total 

costs and therefore did not contribute to heterogeneity of costs among sites. 

Because we were primarily interested in the heterogeneity of costs in space, we 

loaded many of the costs that did not vary greatly by location into the fixed costs. This 

included the initial scoping and planning, treatment design, and permitting. Certain costs 

increase for every day in the field and are not a smooth hourly function, for example such 

as lodging costs, equipment rental, and overtime pay. These costs are handled using the 

Daily Cost (DCk) variable that incremented such costs by the day. 

Based on previous work (Robichaud et al. 2000, Bohlen and King 1995) and 

interviews with restoration practitioners, we identified site and landscape factors that we 

hypothesized would affect heterogeneity of costs across a region. The vector s of site 

characteristics that affected search time (ST) and treatment cost (CAik) influenced each 

treatment type differently. Based on interviews, we determined that site factors that 

affected search time included the infestation size and density, whether the site had 

burned, and the distinctiveness between the invasive and native vegetation. 

Interviews and a literature review also revealed that the factors most likely to 

affect treatment cost included soil type, presence of rocks, proximity to urban areas and 

croplands, protected areas, slopes and aspect (Hesseln et al. 2004). Such factors can 
58 

change the type of equipment used, recommended levels of herbicides and levels of 

safety precautions needed to protect homes or crops, which would translate into more 

hours of labor and materials and alter equipment needs. Areas with sensitive 

environmental resources, such as those in protected areas or the wildland urban interface 

(WUI) would be expected to have higher treatment costs since contractors and agency 

supervisors would need to take extra care to ensure the safety of such resources. Specific 

expenses might include additional supervising personnel, insurance requirements, and 

extra time required for permitting. 

Some site factors did not affect treatment cost when aerial methods were used. 

However, slope remained important in both ground-based and aerial applications since 

slope influences the pattern of application and aircraft altitude, thereby affecting costs. 

Other factors affecting treatment cost were the restoration goals and, in particular, 

whether native or non-native plants were being restored since native seeds tended to be 

more expensive than non-native seeds. 

4.2.1 Treatment Regimes Considered 

In evaluating costs, we considered various levels of treatment intensity for both 

preventative and control treatments. When controlling cheatgrass, the first step in 

treatment is typically to burn the area, therefore, our analysis of burned area rehabilitation 

costs (where treatment is applied to a burned area) was applicable to a broad range of 

treatment currently being conducting. Following a burn, herbicides may be applied 

before reseeding or reseeding may occur without interim treatment. Seeds are spread 

using aerial (fixed wing aircraft or helicopters) or ground-based equipment. Application 

of herbicides can also be spread aerially or using ground-based equipment. Aerial 

seeding is sometimes followed by chaining, where ship anchor chains are dragged across 

the ground surface to increase contact of the seeds with the soil. Mechanical seed 

planting equipment (drill seeders) may also be used and are generally considered more 

effective than aerial seeding. Fencing is used to protect newly seeded areas from 

animals. 

Aspects common to all treatments we investigated were: 1) multiple trips to 

treatment sites were needed to establish extent of potential restoration area (burned or 

infested) and to conduct multiple phases of treatment, and 2) native or non-native seeds 

were chosen based on meeting site-specific restoration goals. Native species, while 

desirable for their hardiness under extreme weather conditions such as drought and their 

ability to support native fauna, are difficult to establish and less competitive with 

cheatgrass than non-native species. Non-native species used to restore sites often have 

forage value (e.g., crested wheatgrass - Agropyron desertorum) and a higher germination 

rate than native seeds. Most commonly, a mix of native and non-native species were 

used, with the proportion of natives varying by site conditions, seed availability and 

management preferences. 

4.2.2 Estimating the Cost of Treatment Model 

We applied statistical modeling, GIS analysis and other estimation methods to 

generate parameters for Equation 9. A statistical model was fit to a database on treatment 

spending for two BLM rehabilitation programs. GIS analyses were used to develop data 

on journey times to treatment sites. 
59 

4.2.2.1 Database on Restoration Spending 

The database used to fit the statistical model of treatment costs contained 

restoration spending information submitted by BLM offices for the Emergency 

Stabilization and Rehabilitation (ESR) and Burned Area Rehabilitation (BAR) programs. 

Projects were implemented from 2001 though 2003 in western states. Included in the 

database were offices in Arizona, California, Colorado, Idaho, Nevada, Oregon, Utah, 

and Wyoming that had implemented projects to mitigate impacts from fires. Cheatgrass 

is being managed cooperatively in this region by USFS and BLM, but all cost data were 

provided by BLM for BLM lands. Collection of spending data was not standardized 

across BLM offices, therefore, we selected data for burned areas in Idaho and Nevada 

only, to limit variability due to different accounting methods. 

The same burned area may receive ESR and BAR funds, so data from both 

programs were combined to more accurately reflect total restoration spending per site. 

Fire numbers were used to combine data from the two sources by location and total 

amount spent in both programs was combined. The combined database for 2001-2003 

had a total of 65 unique observations that included the critical spending and site 

attributes, 35 for Idaho and 30 for Nevada. Database attributes for sites included location 

descriptors, size, and costs of treatment. Treatment spending was broken down into costs 

for aerial seeding, drill seeding, miles of fencing, and herbicide use. The types of seeds 

used (native vs. non-native) and whether native shrubs had been planted were described. 

All sites received aerial seeding over some portion of the burned area and a subset 

received more intensive practices such as herbicide and drill-seeding. The majority of 

sites showed spending on fencing (72%) and this spending was broken out into repair of 

permanent fence or installation of temporary fencing that was either electric or nonelectric. 

4.2.2.2 Data Development within the GIS 

The spending database was joined to a spatial coverage of reported fires (BLM 

2004) to allow rehabilitated areas to be geolocated. The GIS coverage of fire locations 

provided a single point corresponding to fire location. A unique fire ID was available in 

both databases to conduct an accurate linking. 

Using the fire location points to represent the approximate center of the burned 

areas, we used supplemental spatial data and GIS analyses to calculate or associate 

additional attribute variables with each burned area. In cases where we were interested in 

conditions across the entire burned area, we estimated the location of fire extent. 

Because we did not find data on exact fire footprint on the landscape, we assumed fires 

were circular and centered on the point location. Fire size was used to calculate an 

appropriate circle radius. These circular areas were used to determine average conditions 

of variables across the burn, such as average slope, and used to determine presence or 

absence of certain conditions, such as whether the protected areas occurred within the 

burned area. The complete list of variables calculated in the GIS is shown in Table 6. 

Table 6. Variables Developed Using GIS Data and Analysis to Test Effects on Treatment Costs 
60 

Variable Calculation 

Elevation Average value within burned area (DEM from ICBMP 

2004) 

Slope Majority of cells within 0-10%, 10-30%, or > 30% 

slope; calculated from elevation (DEM) data 

Within Urban area or Wildland 

Urban Interface (WUI) 

Co-occurrence with urban land use defined in WUI 

(Radeloff et al. 2005) 

Rocky areas Co-occurrence with “Barren” land category (Idaho 

Gap Analysis, Landscape Dynamics Lab, 1999) 

Within Protected Area IUCN protected status: IA, IB, II, and IV; 

(Conservation Biology Institute 2005, DellaSala et al. 

2001)

Airport Travel Time Travel Time/Cost Analysis (see text) 

Field Office Travel Time Travel Time/Cost Analysis (see text) 

Travel Time Estimation Methods 

To evaluate travel time and costs, we first used a method to determine least cost 

travel paths between locations. An algorithm available within the GIS software selects 

paths between origin and destination cells by minimizing the cumulative time cost of 

travel (ESRI 2005). Travel time between any two cells is calculated by 

 ti = f(Distance, Impedence) (Eqn 10) 

where travel time (t) is a function of cost-weighted distance represented as the impedence 

or friction of traveling between cells. The impedence represents relative travel speed and 

is measured through an impedence map that associates travel speed with each cell on the 

landscape. The impedance map was created using four variables that affected travel time. 

The road network was mapped and road segments were weighted by road class in 

proportion to speed limits by road class. Other variables were added to affect travel offroad. Large streams and rivers were used to create barriers to travel off the road network 

and slopes were used to slow travel in areas with no roads by dividing slopes into three 

classes and weighting travel speed within each class. These factors were weighted and 

combined such that the value of each cell in the impedence map equaled the time 

required per unit distance to pass through the cell (Figure 10). 

The cumulative time to move from the nearest origin point to a destination point i

(Ti) is the sum of the impedence of all the cells along the least-cost route: 

= ∑

i

i i T t

 (Eqn 11) 
61 

Total travel times between points were estimated for several sets of origin and destination 

points. To represent personnel travel times, field offices were used as the origin points. 

Destination cells consisted of all invaded or potentially invaded lands. To represent 

contractor driving time associated with certain treatments, we calculated driving times 

from airports to represent required travel time for contractor vehicles that supported 

aircraft. Invaded and invadable areas were identified using a map we created of 

cheatgrass cover (Appendix A) and by assigning invadability status to current land cover 

(ICBEMP 2004) using best professional judgment of R. Mack who has conducted field 

studies of cheatgrass in the region for over 30 years. Using these origin and destination 

points several versions of travel cost maps were developed (Figure 11).

Figure 10. Impedence Map Representing Travel Time per Landscape Grid Cell 

Map showing the relative time required to travel through an individual grid cell on the landscape. 

Darker shades represent slowest travel times; lighter shades faster travel times. Major roads, 

which had the fastest travel times, appear as white areas. 
62 

Figure 11. Cumulative Journey Time Map 

Map showing the sum of travel times along the “least cost” path between BLM district offices 

and all potential treatment locations. A least cost path is determined through a routing algorithm 

using the impedence map, shown in Figure 10 and then total travel time is the cumulative sum of 

time time along that path. 

4.2.3 Model Estimation 

Our objective with the cost modeling was to identify variables that could explain 

heterogeneity of total treatment costs (TCi) among treatment sites and to develop a model 

that could be used to predict costs for untreated sites. However, the statistical modeling 

that was fit to the treatment spending database could not encompass BLM personnel time 

and other costs because the majority of observations within the treatment spending 

database accounted for materials and contractor costs only (Tom Roberts, pers. comm.). 

As a result, our statistical model only estimated treatment cost per area (CAik) which 

would be able to represent expected contractor bid amounts by location and treatment. 

Planning costs and supervisory costs by agency personnel were estimated elsewhere (as 

described below). 

As previously discussed, we hypothesized that treatment costs would vary due to 

factors affecting material, labor and time costs of treatment. Of the variables we 

identified as affecting costs, we were able to gather data or create methods for measuring 

slope, elevation, presence of rocks, location in protected areas, location in WUI, and 

remoteness (measured as driving time from airports). 
63 

We also expected higher intensity of treatment to increase treatment costs and we 

tested the effects on costs of all treatment options identified in the database including use 

of: drill seeding, fencing, herbicides, and native seeds. We also tested whether 

differences in costs could be attributed to the state from which reports originated. We 

hypothesized such costs might differ due to variations in accounting, treatment, site 

conditions or other factors. 

Economies of scale were anticipated, since larger burned areas would be expected 

to be cheaper to treat on a per acre basis. Previous work has suggested that fire treatment 

costs are a nonlinear function of size of fire. For example, fire suppression costs for large 

fires have been estimated to increase with the square root of fire size (Mills and Bratten 

1988). We tested several nonlinear relationships between average costs per acre of 

invasive species treatment and total size of area treated. The economies of scale would 

be expected to be derived from spreading fixed costs, such as helicopter rental and 

transport to site, across more treated area. 

4.2.3.1 Model Limitations for Prediction 

The database presented many challenges to testing our hypotheses. Foremost in 

terms of estimating the effect of treatment intensity, was that the data on the proportion of 

the fire treated with each treatment methods were missing in many cases. Also, 

information on whether chaining had been conducted was missing. Since treatments 

were applied to very different proportions of the site, and chaining could potentially 

increase costs substantially where used, these were serious omissions. Although, we 

were not able to weight each treatment by area treated, we still chose to examine how use 

of a practice (binary yes/no) affected total treatment cost per acre. 

Other challenges included selection bias in the data set. Using only treated fires 

to estimate costs for all fires is problematic because treated areas are likely to have 

different characteristics from untreated areas. Most troublesome was that more difficult 

sites were likely to be left untreated, creating a tendency within our model to 

underestimate costs for some sites because of effects we did not estimate. Yet, sites with 

high ability to recover naturally were also untreated and treatment costs may be 

somewhat lower in these sites, perhaps creating a competing effect to lessen the degree of 

bias in the model. Most importantly, the model would be expected to be most accurate 

for sites with the highest probability of treatment under current practices. 

Several factors caused us to reduce the number of observations used in the 

statistical model from 64 to 46. We were forced to omit observations that could not be 

associated with points mapped in the spatial database of fire occurrence because of the 

need to measure complementary site attributes within the GIS. Therefore, the number of 

observations was reduced to 48 through this process, resulting in 28 observation within 

Idaho and 20 within Nevada. In addition, only one observation of a treatment using 

hand-planting was available, so this observation was discarded and one extremely 

expensive treatment site (outlier) was removed from the dataset because of concerns that 

this one data point was unduly influencing model results. This site was a particularly 

small burned area. Therefore a total of 46 observations were used in final model 

estimation. 
64 

4.2.3.2 Treatment Cost Model Specification 

Our initial modeling used ordinary least squares (OLS) linear regression, to 

estimate a model of the form: 

∑=

= + +

J

j j y x

j 1

α β ε (Eqn 12) 

Where was a constant, ’s were the estimated coefficients on the independent variables 

(x) and represented unexplained variability. The variable j indexes the independent 

variables used to predict costs. The vector of independent variables tested (x) is shown in 

Table 7. 

Table 7. Variables Considered for Empirical Cost Model 

Variable 

Mean 

(continuous) 

(n=46)

Sum 

(binary) 

(n=46)

Treatment options 

 Fencing use (=1 if used) 34 

 Drill seeding use (=1 if used) 16 

 Herbicide use (=1 if used) 22 

 Native seed use (=1 if used) 29 

 

Site and location characteristics 

 State (=1 if Idaho) 27 

Within WUI (=1 if within) 2 

Within Protected Area (=1 if within) 6 

Slope class (= 0 if 0-10%, =1 if 10-30%, none > 30%) 4 

 Burned area within BLM lands (acres) 4605 

 Elevation (m) 1547 

 Airport Driving Time (hours) 1.16 

 

Dependent variable 

 Treatment cost per acre ($) $102 all cases 

($64 ID, 

$154 NV) 

Variable names shown in gray were not tested in model due to the limited number of 

observations. 

Once the final database had been constructed, it became clear that we did not have 

sufficient observations in some classes to test effects. We quickly eliminated WUI 

location, slope class, and protected area location due to the lack of sufficient 

representation of such conditions. All continuous independent variables (burned area, 
65 

elevation and driving time) were log-transformed, as was the dependent variable of cost 

per acre. 

Using model fit statistics from both ordinary least squares and maximum 

likelihood estimation, a parsimonious model was selected that included five independent 

variables shown in Equation 13. The variables that were dropped: fencing use, elevation, 

and airport driving time either had little predictive value or collinearity problems with 

other variables. The final OLS model had the form: 

ln(cost per acre) = + 1ln(fire size) + 2(state) + 3(herbicide) + 4(drill seed) + 

5(native seeds) (Eqn 13) 

This model had an R2 of 0.608, an adjusted R2 of 0.559 and was significant at > 0.001 

level. Coefficient estimates are shown in Table 8 and, if we assume a valid model, all 

coefficients were significant at p > 0.02, although as we discuss below, these significance 

tests are suspect due to spatial autocorrelation of the residuals. 

Table 8. Coefficient Estimates from OLS Model 

Coefficients Std error 

Standardized 

Coefficients t statistic 

Constant 6.440 0.509 12.649 

State dummy -1.222 0.217 -0.743 -5.620 

Herbicide dummy 0.494 0.189 0.304 2.606 

Ln(Area) -0.306 0.066 -0.485 -4.642 

Drill seed dummy 0.548 0.182 0.322 3.015 

Native dummy 0.562 0.226 0.335 2.488 

The OLS model results suggested that costs in Idaho were lower than in Nevada, 

when treatments applied were held constant. As expected, we found economies of scale 

with treated area size in which cost per acre was a decreasing function of the log of area. 

As part of fitting the model, we explored other relationships between area treated and 

cost per acre and found the log function provided the best fit to the data. Also as 

expected, extra treatments, such as using herbicides and drill seeding, increased per acre 

costs. Native seed use tended to increase costs. 

The effect of state (Idaho vs Nevada) was highly significant indicating that 

treatment methods and or accounting methods were dramatically different between states. 

We combined data from both states to improve statistical power of the cost model and to 

create a more geographically diverse set of treated fires. However, combining data 

between these two states clearly created a less homogenous dataset. 

Unfortunately, none of our location characteristics could be definitively linked to 

costs of treatment. This result was unexpected and we suspect part of the lack of 

predictive power of these variables stems from problems with data. Improved databases 
66 

are needed to fully test the potential relationships and alternative model forms explored. 

The selection bias inherent in our data set appeared to eliminate difficult sites that would 

have higher costs and thus prevented us from testing the effects of difficult conditions on 

cost. The lack of many treated sites in areas where costs would be expected to be high 

(e.g., in urban areas, protected areas, areas with high slopes) suggested, and interviews 

with managers confirmed, that difficult sites were generally avoided. 

0

1

2

3

4

5

6

7

0 2 4 6 8 10 12

LN (Fire Size)

LN (Treatment Cost per Acre)

Figure 12. Natural Log of Cost per Acre vs. Natural Log of Fire Size 

We tested several nonlinear relationships between fire size and treatment costs in our 

statistical model and the log of fire size provided the best fit for our dataset. 

4.2.3.3 Test of Residuals for Spatial Autocorrelation 

Spatial autocorrelation of data can arise when observations are close together in 

space. The minimum distance between burned areas was about 3.75 miles for our 

combined data set for Nevada and Idaho indicating a reasonable separation between data 

points. Nonetheless, we expected to find spatial autocorrelation of the data and a semivariogram plot and a likelihood ratio test confirmed a moderate degree of spatial 

autocorrelation of the residuals from the OLS model. Because of this spatial 

autocorrelation, the parameter estimates for our model are unbiased but inefficient, and 

standard error estimates are biased thereby throwing significance tests into doubt. 

A comparison of methods for dealing with spatial autocorrelation of errors 

demonstrates that significance tests may be strengthened or weakened by failing to 

correct for this bias (Bell and Bockstael 2000). While many statistical tests are available 

to handle such autocorrelation of the errors, decisions made in estimating alternative 

models can produce other sources of bias (See Bell and Bockstael 2000 for a comparison 
67 

of methods and Anselin and Florax 1995 and Cressie 1991 for more complete 

discussion). Given that the selection bias of our data and other questionable aspects of 

the data weakened the strength of our OLS model, we did not expect the benefits of 

correcting for spatial autocorrelation of the errors to warrant the extra effort of fitting a 

different model. Rather, for this screening effort, we used the OLS model to estimate 

costs at untreated sites with the acknowledgement that this estimate could be improved. 

In the future, expected improvements in cost accounting databases will likely warrant 

such efforts to develop a model robust to spatial correlation errors. 

4.2.3.4 Other Sources of Cost Data 

We made the simplifying assumption that fixed costs were the same for all 

locations; therefore variation in costs between sites was determined by variable costs 

only. Because of poor data availability, we did not include a value for fixed costs in our 

total cost calculations. This omission has the effect that cost-effectiveness ratios will 

appear higher than if we had included fixed costs. However, this omission does not 

affect the budget constraint of the optimization or of the real world decisions of resource 

managers because the agency’s treatment budget does not include fixed costs. 

Search Costs 

For the types of treatments applied here, where large burned patches were being 

treated, search costs (i.e., for invasive plants of interest) were ignored since individual 

plants or patches of infestation were assumed to be readily identifiable. However, search 

costs may be significant when only parts of patches are being treated. 

Journey Costs and Daily Costs 

We created coefficients for journey costs (JCk) and daily costs (DCk) by 

examining published reports, grey literature analyses of treatment costs, and previous 

databases we had created for restoration costs. In addition, we interviewed personnel 

within local field offices to gather additional information regarding practices and costs 

not directly associated with treatment such as personnel time and hourly rates. Overhead 

costs were ignored because they did not contribute to major heterogeneity of costs 

between sites. Fixed costs such as initial scoping and planning, treatment design, and 

permitting were included to a limited extent as an initial site visit with personnel and 

equipment costs. Information on fixed costs was not readily available from accounting 

personnel. 

Comprehensive information about personnel costs was not available from BLM, 

but a representative from the Twin Falls district described typical makeup of crews that 

would visit sites for planning and contractor supervision. A typical initial site visit might 

be conducted by 6-7 people, typically all GS-11s. Once contracts are in place for 

treatment, 3-5 people will generally have responsibility for inspecting sites and 

supervising contractors depending on the number of contracts issued. Different 

treatments require different crew make-ups. From this information, we estimated 

average, low and high hourly costs to represent different types of crews visiting a site. 

The journey costs by treatment (JCk

) used for subsequent modeling and shown in 

Table 9, incorporated the average hourly crew rate for initial inspection and one followup inspection trip. A per vehicle cost of $0.315/ mile was applied, based on the IRS 
68 

reimbursement rate for large vehicles such as vans or trucks. Daily costs were not used 

because sites were not sufficiently far from offices to indicate BLM personnel would be 

required to stay overnight. 

4.3 Cost Model Discussion 

The importance of cost-screening tools should not be underestimated since a 

manager typically decides which sites to treat based on little or no explicit cost 

information. Much of the treatment work is contracted to outside businesses and 

therefore, according to BLM personnel, the details of cost estimation are not well 

understood within the agency. Also, the cost of personnel time to administer contracts 

and monitor sites is not well-tracked. Clearly, if effort is going to be allocated based on 

cost-effectiveness of all direct and indirect costs, improved accounting would be needed. 

We were able to generate tools to estimate costs of treatment at untreated sites by 

creating 1) estimation equations of treatment costs by treatment intensity and 2) maps of 

journey time that could be created within the GIS and combined with personnel and 

vehicle costs (Table 9) to generate journey costs for agency personnel and equipment. It 

was likely our cost model underestimated total costs because of the variables we were not 

able to include. 

The statistical modeling exercise of treatment cost per acre did not find that site or 

location characteristics were useful for predicting costs by location. This result is in 

contrast to other work that found that site characteristics were important in predicting 

costs (Hesslen et al. 2004). We attributed our inability to link site characteristics to costs 

to problems with the data that likely prevented us from uncovering these relationships. 

However, through the journey cost analysis, we captured a major factor determining 

variability of cost by location. 
Table 9. Journey Costs per Hour and per Trip 

Treatment level (k) 

# 

trips 

# 

vehicles

Vehicle 

operation 

cost 

($/hr)

Average 

cost crew 

($/hr)

Low cost 

crew 

($/hr)

High cost 

crew 

($/hr)

Inspection 

crew cost 

($/hr)

No Treatment Aerial seeding only 1 1 $18.90 $160.59 $114.56 $206.61 $34.61 Aerial seeding + chaining 2 1 $18.90 $160.59 $114.56 $206.61 $34.61 Aerial seeding + chaining + herbicide 3 1 $18.90 $160.59 $114.56 $206.61 $34.61 Aerial seeding + chaining + drill-seeding 3 1 $18.90 $160.59 $114.56 $206.61 $34.61 
70 

5. Restorability 

5.1 Introduction 

The benefits of post-fire rehabilitation are inextricably linked to the successful 

outcome of such efforts. The perceived value of the investment, as with any risky 

investment, depends on the certainty of the outcome. For a typical risk-averse investor, 

risk reduces the perceived expected value of an investment, and the reduction in value is 

a function of 1) the degree of risk as measured by the variability of potential outcomes 

and 2) the degree of risk aversion of the investor. This means that, all else equal, riskaverse managers will prefer to do a restoration that is a “sure thing” rather than pursue an 

option that has a high probability of failure. 

How might we take the effect of risk into account when weighing alternative 

investments? The basic formula investors use for comparing uncertain outcomes is to 

weight expected value by the probability of alternative outcomes using a formulation 

such as: 

 E(B) = [ succeed

ijk b * p] + [ failijk b * (1- p)] (Eqn 14) 

where the expected value of benefits E(B) is the sum of the expected benefits of each 

alternative outcome (bijk as measured if the project succeeds or if the project fails) 

multiplied by its probability of occurrence. If there are only two outcomes, success and 

failure, and p is the probability of success, then the probability of failure is 1- p. The 

benefits of a successful project are multiplied by the probability of success and the 

benefits of failure are multiplied by the converse probability, allowing the total expected 

values of outcomes to be estimated. This model provides the decision-maker with a 

logical means to compare benefits for projects that vary in risk levels. 

Success of restoration depends on how success is defined. The broad 

management goals may be to reduce erosion potential, to limit the cover of invasive 

species and to restore vegetation appropriate to the expected uses of the site. Areas with 

the potential to provide quality habitat may have additional goals set forth to establish 

native species, whereas site with limited ability to provide habitat may still serve as 

productive areas for livestock grazing or other uses. 

In the case of restoring a burned area, success was defined, through discussions 

with managers and scientists, as several sub-goals that would allow the overarching goals 

to be realized: 1) preventing regrowth of cheatgrass that was present before the fire, 2) 

preventing new cheatgrass recruits from establishing, and 3) ensuring long term survival 

of desirable species, which may be natives or non-native forage species (Figure 13). 

Many factors had the potential to affect the probability of success of each sub-goal. We 

identified three general categories of factors that determined restorability, or probability 

of success: site characteristics, location or landscape characteristics, and stochastic 

variables such as rainfall patterns. Each category had a main influence on one of the 

three sub-categories of success and a lesser effect on the other categories as shown in 

Figure 13. 
71 

Figure 13. Influence Diagram of Restorability 

The overall probability of success (circle at far left) was conceptualized as the joint probability of 

1) preventing regrowth of cheatgrass present before the fire, 2) preventing new cheatgrass recruits 

from establishing, and 3) ensuring long term survival of desirable species (natives or non-native 

forage species). The probabilities (circles) in center column were functions of the observed 

factors (parallelograms and a circle in rightmost column). Site variables included characteristics 

such as % cover of cheatgrass pre-fire and elevation. Landscape variables included factors such 

as distance to nearest cheatgrass-infested area. Stochastic determinants included factors such as 

timing and quantity of rainfall, and availability of experienced pilots. Width of arrows shows 

relative importance of a given type of factor in determining the probability. 

Restorability was not considered to be independent of treatment effort. Given 

unlimited resources, almost any site can be successfully restored unless we lack technical 

knowledge or source materials. Such a case of irreversibility appears to exist, for the 

moment, in parts of Southern Nevada. Fire now occurs regularly in a landscape that did 

not evolve in the presence of regular fire. It appears that following fire, an invasive nonnative grass, red brome (Bromus rubens), is increasing its range and prevalence; 

cheatgrass may also be adapting and invading into the Mojave desert in southern Nevada. 

As a result, plants have limited capacity to rebound following fire and we currently lack 

the materials and expertise to propagate the plants that are being lost (T. Roberts pers. 

comm.). Nevertheless, in many systems invaded by non-native plants, we expect to be 

able to increase the probability of successfully restoring services by increasing the level 

of inputs, although a non-linear (e.g., exponential) relationship between inputs and 

success is typical (Figure 14). 

Probability 

of 

Success 

Site 

Variables 

Landscape 

Variables 

Stochastic 

Variables 

1. 

Probability 

of 

Cheatgrass

Regrowth 

2. 

Probability 

of New 

Cheatgrass 

Infestation 

3. 

Probability 

of Native / 

Forage 

Growth 
72 

Figure 14. Reversibility of System Decline 

Theoretical representation of ecosystem service output after restoration as a function of level of 

degradation (% invasive cover) before fire. The solid white line shows the ecosystem service 

outputs after restoration. The blue line shows the increasing inputs required to achieve the level 

of restoration shown. The dashed lines show the range of potential outcomes and increasing 

uncertainty of outcomes at higher levels of initial degradation. 

5.2 Measuring Recoverability and Restorability 

Returning to Equation 3, we developed Sik (restorability) as a function of natural 

recoverability and treatment effectiveness. 

 Sik= ri + k (Eqn 15) 

 ri = site recoverability 

 k = treatment effectiveness 

 i = site 

 k = treatment applied 

Thus, we envisioned restorability as a function of site characteristics that tended to 

increase or decrease the probability of success for a given treatment type. Note that in 

the absence of treatment, recoverability = restorability (S=r). 

We found, as others have (Robichaud et al. 2000, Eiswerth and Shonkwiler 2006), 

that little empirical evidence exists to quantify probabilities of successful restoration of 

cheatgrass invaded sites. Even less information was available on the ability of systems to 

recover naturally, let alone provide information on variables that would affect variability 

of response. Therefore, we used a combination of techniques to identify conditions that 

might be predictive of restoration outcomes. A literature review and interviews with 

managers and researchers provided initial information which we used to develop an 

interview protocol to guide further discussions with managers. Within interviews, we 

encouraged managers, ecologists and restoration practitioners to weight the relative 

importance of different factors (Appendix B). We also informed our restorability 

% invasive cover (pre-fire)

PostRestoration 

Ecosystem 

Service 

Output 

Site i

Input(s) 

$
73 

analysis through a statistical exploration of the qualitative restoration outcomes included 

in the treatment spending database used for the cost modeling. 

Our goal in developing data for recoverability was to characterize biophysical 

attributes that could be mapped to allow managers to weight risk of benefits within our 

spatial cost-effectiveness screening tool. Our ideal data set for testing such biophysical 

factors, would have included multiple sites with varying site conditions and located 

within different environmental contexts, for each level of treatment applied. In other 

words, we would like inputs to have been held constant as we compared the probability 

of success across environmental gradients. However, the concepts of recoverability and 

treatment effectiveness were confounded in the database we examined and in the expert 

judgment we elicited from managers because treatment was applied as a prescription, 

tailored to site conditions. Managers, quite reasonably, adjusted treatment inputs in an 

attempt to hold probability of success more or less constant. This limited our ability to 

statistically analyze the data, and therefore we relied more on interviews to try to tease 

apart the effects of treatment vs. site conditions. 

5.3 Literature Review of Restorability Data 

We reviewed the literature for information on factors that affected the ability to 

control cheatgrass and to characterize the effectiveness of restoration practices and 

invasive species control techniques. Most of the information was available only as grey 

literature and not within peer-reviewed publications. 

5.3.1 Restoration Techniques Effectiveness 

The most systematic review of restoration techniques we found was an analysis 

by Robichaud et al. (2000) who examined the effectiveness of post-fire rehabilitation, in 

western Forest Service lands, for preventing erosion and establishing vegetation. They 

reviewed 321 restoration projects put in place over 26 years and evaluated relative 

effectiveness of specific techniques in addition to the effects of site and environmental 

factors contributing to success or failure of projects. Much of the evidence was drawn 

from post-fire monitoring reports, although interviews were also used to supplement 

reported data. 

The Robichaud et al. work identified a variety of factors that might limit or 

enhance effectiveness ofpost-fire seeding including the ability to find proper inputs such 

as: contractors and aircraft operators, weed-free straws, and skilled pilots. Their work 

suggested that timing of seed application was important because it could affect 

probability of experiencing favorable weather such as rainfall and avoiding negative 

events such as high winds after seed placement. Other factors that tended to enhance 

success included successful protection from grazing (a combination of low existing 

grazing pressure and reducing pressure through effective fencing), avoiding slopes, and 

avoiding soils that were shallow, rocky, uneven or fine-textured. 

 
74 

The reported effectiveness associated with seeding tended to be higher when 

qualitative techniques were used to judge results and lower when quantitative techniques 

were used. Around half of the interviewees and monitoring reports that used quantitative

information stated that aerial seeding had good or excellent effectiveness. On the other 

hand, 79% of monitoring reports using qualitative judgments considered seeding 

successful in the first year following fire (Robichaud et al. 2000, p. 45). 

The same report showed that reported effectiveness also varied by geographic 

region. Reports from the region that including Idaho showed a higher proportion of 

responses stating that seeding was effective compared to other regions of the country. 

However, it should be noted that many of the restoration sites evaluated were in locations 

with higher precipitation levels than the case study sites examined in southern Idaho. 

The difference in aerial seeding success rates perceived by those using qualitative 

vs. quantitative information, speaks to the need for more rigorous studies to determine 

effectiveness. In Robichaud et al.’s review of treatment effectiveness, they found the 

literature “limited.” In terms of evaluating natural recoverability of sites, they also found 

that, “good methods for assessing native seed bank viability are lacking.” 

A study of restoration success that focused exclusively on rangeland in Nevada 

(Eiswerth and Shonkwiler 2006) used an empirical analysis to evaluate seeding success 

of natives and non-natives as a function of site conditions and seeding techniques. They 

found that 1) timing of seed placement 2) seeding rate and 3) whether grazing had 

resumed between fire and seeding were most predictive of success. Seeding was most 

successful in the fall and early winter. They also found the response to seeding rate was 

quadratic, indicating success peaked at an intermediate seeding density. Grazing between 

the fire event and seeding appeared to enhance cover of cheatgrass. From the limited 

database at their disposal, they were able to develop initial empirical relationships 

between site conditions and treatment effectiveness, but further work is needed to test 

these effects across regions. 

A few other studies have tried to determine what makes arid grasslands 

susceptible to cheatgrass invasion. For example, Gelbard and Belnap (2003) found that 

sites within 50 meters of a paved road had a higher proportion of cheatgrass cover than 

sites adjacent to unpaved four-wheel drive tracks. The effect of elevation has been 

studied and there seems to be some consensus that some elevation threshold generally 

exists above which cheatgrass does not persist and that higher elevation is also associated 

with higher probability of successful recovery and restoration (Pyke et al. 2003, 

DiTomaso 2000). However, consensus on the exact elevation of the threshold is elusive 

and may vary by region. 

5.3.2 Control Effectiveness 

We evaluated literature that examined effectiveness of various mechanical, 

chemical, and biological control methods. Much of the literature involved observations 

on limited numbers of plots, often without control plots, and therefore the results were of 
75 

limited use. However, we found reasonable documentation and quantitative studies on 

the effectiveness of herbicides to control cheatgrass and other invasives, most likely 

because it is a primary method of weed control in rangelands (DiTomaso 2000). 

Although most studies did not consider the effect of location on effectiveness, one study 

identified precipitation regime as an important restorability marker (Quigley et al. 1996). 

For cheatgrass control, two studies showed that the herbicide OUST® 

dramatically reduced cheatgrass cover on treated sites. Studies showed that timing of 

application affected success with 95% control achieved on fall-treated and 60% control 

achieved on spring-treated. The treatment was more effective on a weed that typically 

co-occurs with cheatgrass, medusahead (Taeniatherum caputmedusae ssp. asperum), 

resulting in a 93% reduction in biomass on fall-treated and 82% on spring-treated plots 

(Shaw and Monsen 1999). Pellant et al. (1999) reported that OUST® was more effective 

than disking, burning or no treatment on research plots in Nevada. The herbicide 

treatment resulted in a 26% “frequency of occurrence” of cheatgrass compared to 72% 

occurrence on the control plots and 46% or 42% occurrence on the disked and burned 

plots. 

The herbicide OUST® is no longer used by BLM to control cheatgrass, but they 

have sought permission to use another herbicide, Imazapic (Plateau®) (BLM 2005), and 

in the interim are using glyphosate (Roundup). We did not find any published studies on 

the effectiveness of these herbicides for controlling cheatgrass but we were told by 

researchers that both herbicides have the potential to be highly effective, with Plateau® 

offering residual (long-term) control (J. Volmer pers. comm., M. Pellant pers. comm.). 

5.4 Using Elicited Best Professional Judgment to Score Restorability 

Although we identified many factors that had the potential to affect restoration 

probability, the restoration practitioners and researchers we interviewed generally 

focused on only a few of the variables as being most appropriate for generating rules of 

thumb. The response of practitioners to early interviews steered us away from pursuing 

the use of a more structured survey instrument. Several factors contributed to a lack of 

enthusiasm for investing our research resources in a survey. First, empirical data were 

largely lacking and restoration practitioners appeared to have insufficient experience or 

information to judge potential success objectively, particularly given the high variability 

of annual grass growth. Second, only a subset of researchers were comfortable 

generalizing about conditions, especially since they viewed groups of conditions as being 

the most important determinants. Many could not isolate individual factors for 

evaluation, indicating that a complex survey design was needed (e.g., a contingent choice 

model), which would, in turn, necessitate having many respondents. Third, restoration 

experiences tended to vary with the particular ecosystem/ecoregion under study. 

Therefore, the number of researchers or practitioners with expertise in any particular 

system was limited and likely to preclude successful implementation of a complex 

survey. 
76 

We used the interview protocol we developed (Appendix B) to generate 

discussion and elicit responses from a variety of personnel engaged in restoration of 

rangelands. The group included biologists, ecologists, economists, program managers, 

and rangeland specialists and represented agencies including the USDA Forest Service, 

Bureau of Land Management, US Fish and Wildlife Service, and US Geological Survey 

and academic institutions. 

The broad range of interviews or group discussions we conducted, among 

approximately 30 restoration practitioners, yielded the results in Table 10. To refine 

those results, we examined which variables were highly correlated spatially and found 

substantial overlap. The correlations allowed us to identify some variables as potentially 

redundant, however, we were not able to elicit sufficient information to allow us to 

combine remaining factors into a cohesive model of restorability. 

Using these results and interviewee comments, we adapted our interview protocol 

to focus on the most important factors practitioners used when selecting appropriate sites 

for treatment. We interviewed restoration practitioners within the Twin Falls BLM 

district and gave significant weight to their judgments since they had the most experience 

conducting restoration in these ecosystems. As previously mentioned, restoration 

practitioners tended to adjust treatment to expected site outcomes and therefore used 

restorability “rules of thumb” to set treatment levels. For example, managers would use a 

higher proportion of native seeds on sites they deemed to have a higher probability of 

success and were more likely to use herbicides on sites with a low probability of success. 

In addition to identifying which factors affected success of treatment, we asked managers 

to identify factors and thresholds of such factors that would reflect the likelihood of a site 

to recover on its own (recoverability). 
77 

Table 10. Restorability Factors Rated by Restoration Practitioners (based 

on interviews)

High 

Restorability

Moderate 

Restorability

Low 

Restorability 

Precipitation zone 

(thresholds vary by locale) 

 < 8 in (20 mm) X 

 8-14 in X 

 > 14 in (36 mm) X 

Cheatgrass cover 5-20% X 

Cheatgrass cover >20% 

existing on site X 

Elevation 

 >6000 ft. X 

 5000-6000 ft X 

 3000-5000 ft X 

Human Use 

 urban use X 

 intense recreational use X 

Soil Type 

 droughty soils (sandy or 

granitic)* X 

 high clay content soils* X 

Ownership fragmentation 

(private landowner) X 

Habitat type 

 Mountain big sage X 

 Wyoming big sage X 

 Salt desert shrub X 

* Opinions differed on the effect of soil texture; high clay content (the opposite 

of droughty soils) was seen as an indicator of low restorability by some 

restoration specialists. 

5.5 Statistical Evaluation of Restorability Data 

The same database used to evaluate costs of treatment included some rudimentary 

information on restoration outcomes. We used that data on treatment outcomes to fit an 

empirical model that we hoped would allow us to predict probability of successful 

restoration. However, the database had significant limitations. The developers of the 

treatment database cautioned us that the data were not highly robust since they were 

gathered from numerous reporting sources and observations were missing for many 

variables. This warning from the database developers, and our own evaluation of the 

database, led us to limit our interpretation of the statistical findings for making 

predictions. However, we cautiously present the results of our statistical modeling to 

show how future data collection could be used to inform restorability and recoverability 

models. 
78 

The outcomes of restoration were described qualitatively by managers and we 

coded that information to allow us to conduct statistical modeling. Project results were 

judged by BLM managers using qualitative terms of “excellent”, “very good,” “poor,” 

etc., which we assigned to a 0-5 scale with 0 being failure and 5 being “excellent” results. 

By assigning a 0-5 scale to the qualitative descriptions, we were able to put results in 

rank order and conduct statistical modeling to test whether the independent variables we 

had identified explained variability of successful outcomes. 

Using ordinal logit (maximum likelihood) regression analysis, we explored the 

relationship between success ranking (0-5) and selected independent variables (Table 11). 

We tested the explanatory power of the site and landscape variables, treatment variables, 

and total spending to predict success rate. Treatment variables were included so that 

contributions of site conditions to restorability could be tested while controlling for 

treatment effort. Since we did not have data for untreated sites, we were not able to 

independently estimate natural recoverability and restorability, however the data offered 

some insights on these distinctions. 

As with the cost modeling, we developed a database of spatial characteristics that 

had been identified as potentially important for predicting restoration success. We 

queried the GIS data to generate five site/landscape parameters identified by practitioners 

and researchers: elevation, slope, percent cover of cheatgrass prior to burn, isolation 

from human activity and proximity to roads. Precipitation regime and the particular 

sagebrush community, which were also identified as important restorability markers, 

were omitted due to high correlation with elevation. 

Several spatial variables were measured indirectly. Our map of cheatgrass cover 

used a binary presence/absence variable and did not include the proportion of cover in 

cheatgrass. Therefore, to estimate proportion of site cover in cheatgrass, we evaluated 

the proportion of the surrounding landscape (fixed window) in cheatgrass and used that 

value as a proxy for percent cover on site. Isolation from human activity was measured 

as driving distance from the closest airport. A site was designated as near a road if it fell 

within a 500-m buffer of a primary or secondary road. 

We controlled for size of treated area and treatment effort by including fire size 

and spending per acre. We evaluated all aspects of treatment choice for their influence 

on restoration success including techniques for spreading seeds, herbicide and fencing 

use, and whether native seeds and shrubs were used. As mentioned in our cost model 

fitting, explicit use of chaining was not available within the database as provided. The 

use of native seeds for grasses and/or shrubs was of particular interest because of the 

anticipated lower success rate in germinating such seeds. Treatment cost per acre and 

fire size were transformed by taking the natural log because of expected non-linear 

responses. We explored interaction terms between variables where we expected to see 

such effects. 
79 

Table 11. Variables Used in Restorability Statistical Model 

Variable 

Mean 

(continuous)

(n=45)

Sum 

(binary)

(n=45)

Treatment options 

 Fencing use (=1 if used) 31 

 Drill seeding use (=1 if used) 15 

 Herbicide use (=1 if used) 21 

 Native seed use (=1 if used) 28 

 Shrub use (subset of native seed use) (=1 if used) 26 

 Spending per acre ($) 89 

Site and location characteristics 

 State (=1 if Idaho) 26 

Slope class > 30% (1 if true) No 

observations 

Within 500m of primary or secondary road (1 if true) 1 

 Proportion neighborhood in cheatgrass 0.29 

 Burned area within BLM lands (acres) 4684 

 Elevation (m) 1544 

 Airport Driving Time (hours) (remoteness) 1.17 

Dependent variable # 

observations 

 Restoration Success (based on manager rankings) 

 0 = Failure 8 

 1 = Poor 13 

 2 = Mixed and Poor 6 

 3 = Mixed and Fair 11 

 4 = Mixed and Successful 1 

5 = Excellent (removed) 2 

Variables in grey were not used in fitting model. Variables with known collinearity issues were 

tested separately (specific cases were 1) native dummy or shrub dummy; 2) spending per acre or 

treatment dummies). 

5.5.1 Statistical Results 

Developing a robust model with good fit statistics was challenging because of the 

many data issues. To explore the small data set, we fit a model with the fewest number 

of variables to understand the strongest correlations and to avoid overfitting the model. 

The best minimal model is shown in Table 12. The model was significant at p > 0.01, 

however, model fit statistics were barely adequate. Observations were insufficient to test 

the five levels of success we included in the model. Aggregating success rankingsinto 

three categories did not improve the model fit. 

Despite the weakness of the model, the signs on the coefficients of the variables 

shown in Tables 12 and 13 were generally robust to model specification. Coefficients on 

native seed use, ln(fire size) and proportion of the landscape in cheatgrass were 
80 

significant in many versions of the model. As expected, native seed use tended to reduce 

restoration success, as did larger fire size and greater proportion of the landscape in 

cheatgrass. Use of fencing tended to increase success and, as expected, being farther 

from an airport tended to increase success. We expected more remote sites to have 

higher probabilities of success, all else equal, due to the generally lower level of 

disturbance and lower cheatgrass cover of sites remote from human activities. All of 

these results were quite tentative and further modeling is required to confirm these 

relationships. 

Table 12. Parameter Estimates for Ordinal Logit Model of Restoration Success 

Estimate Std. Error Wald Sig. 

Threshold [SUCC_RATE = 0] -5.412 2.125 6.488 .011 

 [SUCC_RATE = 1] -3.586 2.068 3.008 .083 

 [SUCC_RATE = 2] -2.749 2.044 1.808 .179 

 [SUCC_RATE = 3] -.486 1.972 .061 .805 

 [SUCC_RATE = 4] .462 1.998 .053 .817 

Independent 

Variables 

Proportion 

cheatgrass -2.208 .980 5.076 .024 

 LN(fire size) -.563 .256 4.824 .028 

 Airport driving time .755 .551 1.882 .170 

 Native seed use = 

false 2.217 .752 8.687 .003 

 Fencing use = false -.495 .800 .383 .536 

Variables dropped from the model included elevation which was not significant 

and the sign on the coefficient was sensitive to model specification. We hypothesized a 

relationship between cheatgrass and elevation but the effect of this interaction term was 

minor in the model. Similarly, drill seed use and herbicide use, which were used on a 

small proportion of sites, did not appear necessary to the model. However, when we 

tested these variables, the coefficients on herbicide use and drill seed use were 

consistently negative (Table 12 shows positive coefficients for not using these practices), 

indicating their use was associated with lower success rates. If these results can be 

believed, they suggest that greater intensity of treatment was associated with lower levels 

of success. This result was not completely surprising given that managers were likely to 

expend more effort on more challenging sites. 

Table 13. Summary of Restorability Model Results 

Reduced Success 

(negative coefficients) 

Enhanced Success 

(positive coefficients) 

% cover cheatgrass Fencing use 

Increasing fire size Driving distance from airport (remoteness) 

Native seed use Elevation 

Herbicide use 

Drill seeding use 
81 

The dummy variable used to test for differences between Idaho and Nevada was 

significant in some models, but the sign on the coefficient varied depending on which 

variables were included in the model. Therefore, even though Idaho had a greater 

number of failures (success = 0 or 1) and Nevada had more successes (success rating 4 or 

5), their practices were sufficiently different that no clear pattern of greater success or 

failure emerged when different site and treatment factors were included in the model. In 

other words, depending on which treatment factors were being held constant, each state 

could be seen to have had relatively more success or failure. This difference likely stems 

from greater use of native seed in Idaho which tended to lower the overall success rate 

unless treatment factors were considered (Figure 15). 

Figure 15. Seed Type (Native vs. Non-Native) and Project Success (2001-2003) 

Use of any proportion of native seeds was associated with lower success rates compared 

to sites using entirely non-native seeds. 

We did not consider the statistical modeling sufficiently robust to use the results 

to predict restorability. We also note that this model suffers from the same selection bias 

present in the treatment cost model. The selection bias resulted from managers being 

more likely to treat sites they thought had high probability of success. Therefore 

predictions made with the restorability model for a randomly selected site might 

overestimate the probability of success. 

5.5.2 Operationalizing Restorability Results 

Due to the limitations of the restoration database and the effect of those data 

limitations on statistical modeling, we did not apply the model results in our restorability 

estimates used in the cost-effectiveness and optimization modeling. Instead, in the 

0

2

4

6

8

10

12

# Sites

012345

Success Rating

Native

Non-Native
82 

interest of providing usable estimates of restorability, we focused on the apparent 

consensus among practitioners and researchers that the percent of cheatgrass pre-fire was 

one of the most important predictors of restoration success. For this variable, we were 

able to elicit probabilities of success from practitioners for multiple levels of the variable 

in order to hypothesize generalized response functions for 1) natural recovery and 2) 

restorability with treatment intensity. The example curves shown in Figure 16 represent 

expected responses of burned areas to recovery or treatment using the pre-fire cheatgrass 

cover as the only predictive variable. This approach of basing restorability on a single 

variable may tend to bias the overall level of success and including more variables could 

show that probabilities are higher or lower for different combinations of site conditions. 

0%

20%

40%

60%

80%

100%

0% 20% 40% 60% 80% 100%

Percent cheatgrass cover (pre-fire)

Probability of success

recoverability

restorability at kmax

Figure 16. Hypothesized Relationships between % Cheatgrass Cover Pre-Fire and Natural 

Recovery or Restorability with Maximum Treatment Intensity 

These relationships were developed through interviews with managers, a literature review and 

statistical exploration of a treatment success database. Restoration success was defined as 

establishing complete or near-complete cover of desirable plant species 2-3 years following the 

highest level of treatment (kmax) and restorability was the expected value of proportion of native 

cover. Desirable plants may include native or forage species. Note that this graph shows the 

contribution of only one factor of restorability; other factors were identified that might increase or 

decrease expected restorability at sites. 

The curves created to judge response of sites to treatment were informed by our 

interviews with restoration practitioners, our literature review, and our statistical 

exploration of the treatment database, but were not a statistical fit of any data source. 

Therefore, these relationships should be used with caution, since they represent 

hypothesized relationships rather than those explicitly demonstrated through field studies. 

The weakest element of these response curves is that we had extremely limited 

information available to distinguish recoverability from treatment effectiveness and had 

to rely completely on opinions of practitioners. For treatment effectiveness, we used both 

available literature studies and best professional judgment of practitioners. 
83 

As shown in Table 14, the restorability relationships showed slightly increasing or 

a leveling off of probability of success as treatment intensity increased. These 

relationships would seem to contradict the results of the statistical analysis that suggested 

that increased intensity of treatment (use of drill seeding and herbicides) was associated 

with lower levels of success. However, we were able to rectify these seemingly 

conflicting findings by determining that managers will generally increase treatment 

intensity on sites they believe have lower recoverability. This reasonable approach to 

determining treatment has the unfortunate side effect of confounding treatment 

effectiveness and recoverability. The relative importance of site factors contributing to 

recovery vs. treatment effects will only be clarified by objective observation of treated 

and untreated sites under a variety of site and landscape conditions. The relationships we 

used here are based on the best, albeit weak, evidence available at this time.5 

Table 14. Probability of Treatment Success by Treatment Intensity Given Percent Cheatgrass 

Cover Pre-Fire 

Treatment Intensity 

Cheatgrass 

cover No Treatment 

Aerial seeding 

only 

Aerial seeding 

plus chaining 

Aerial seeding, 

chaining & 

herbicide 

Aerial seeding, 

chaining & 

drill-seeding 

0% 95% 100% 100% 100% 100% 

10% 50% 65% 75% 75% 75% 

20% 25% 35% 40% 45% 50% 

30% 10% 21% 24% 27% 30% 

40% 2% 7% 8% 9% 10% 

50% 0% 0% 0% 0% 0% 

60% 0% 0% 0% 0% 0% 

70% 0% 0% 0% 0% 0% 

80% 0% 0% 0% 0% 0% 

90% 0% 0% 0% 0% 0% 

100% 0% 0% 0% 0% 0% 

The restorability curves represented the proportion of treatments likely to result in 

“success.” A specific definition of success was not available from our management 

partners, although it was clear that the goal was to prevent all cheatgrass growth where 

possible and achieve as low a percent cover of cheatgrass where complete prevention was 

not possible. Given this conceptual model of success, we used the restorability values we 

derived to generate the expected post-treatment cover of natives using this formulation: 

 Native cover (%) = 1 * Sik (Eqn 16) 

where 1 represents the successful outcome (100% native cover) and Sik is the probability 

of success. Therefore, the expected returns are expressed as percent native cover. 

 

5

 Efforts are underway at BLM to improve reporting of treatments applied and success rates (Tom Roberts, 

pers. comm.) 
84 

Because of the high uncertainty associated with the restorability of sites, we 

eventually framed restorability as a stochastic variable when implemented in the 

optimization software. Using a Monte Carlo function, we defined the restorability as a 

value drawn randomly from a histogram probability function. The histogram probability 

was defined using a normal probability function and the estimated restorability at the 

mean. Making the substitution of the stochastic equation into Equation 16 yields: 

 Native cover (%) = ⎥

⎦

⎤ ⎢

⎣

⎡ = ∑=

6

1

1* ( ) z

ik z z E (Eqn 17) S p s

where E(Sik) represents the expected value of the discrete random variable s. The 

probability of a value occurring within any range of restorability values (i.e., within bin z)

is represented by pz a value between 0 and 1, where the sum of the pz’s equals 1. Using 

Equation 17 to define restorability effectively generates a value for native cover for a site 

that represents an average site response assuming many implementations of the same 

treatment. This result was used to weight benefits of treatment as calculated in Equation 

1. 

5.6 Restorability Model Discussion 

It was clearly a concern that the main variable used for assessing restorability was 

a variable for which we lacked spatial data. However, within a field office conducting 

such treatments, managers are able to develop this information for individual sites after 

fires. Ecologists are readily able to examine the site after a fire and determine pre-fire 

vegetation. Our estimate of regional cheatgrass cover was therefore only a place-holder 

value for proportion of neighborhood in cheatgrass, a variable that can be readily 

supplied through site visits. However, the lack of regional datasets on invasive cover is 

an impediment to conducting screening analyses or comprehensive regional planning for 

invasive management. In some areas (Peterson 2003), cheatgrass density has been 

mapped through remote sensing, demonstrating the possibility that such data could be 

developed comprehensively for other arid regions. 

Perhaps the most important thing we learned from developing the restorability 

models was that treatments were only able to improve outcomes over a small range of 

site degradation. Sites with extremely low percentages of cheatgrass appeared to have 

the potential to recover on their own while sites with greater than 20% cheatgrass cover 

pre-fire had less than a 50:50 chance of recovery, even with the most intensive treatment. 

Pursuing treatment in most cases appeared highly unlikely to generate successful 

outcomes in most cases. 
85 

6. Optimization Modeling to Select Treatment Sites and 

Treatment Intensities 

The models and information developed to measure benefits, costs and 

restorability of treatment options were implemented within an optimization framework to 

explore results and identify sets of options (site and treatment combinations) that could 

maximize various benefit measures subject to a budget constraint. 

6.1 Optimization Model Background 

 Optimization is a basic form of decision-making and, most generally, involves 

allocating scarce resources to meet competing objectives. Optimization may be as simple 

as choosing the shortest route to get from Point A to Point B in order to meet the 

objective of minimizing time and cost. However, optimization questions can become 

complex quickly as the number and range of resources and options for achieving 

objectives and, in some cases, the weights given to competing objectives increase. 

 In the application that will be described in the following section, for example, the 

optimization problem involves allocating limited dollars, labor, material, and equipment 

to different locations and sizes of burned areas in order to maximize the outcomes of 

cheatgrass preventative treatment. The objective being maximized in this case is a set of 

sometimes competing environmental and economic goals (e.g., improved wildlife habitat 

vs. improved livestock grazing). The optimization model was run using a variety of 

weights assigned to individual goals in order to test the sensitivity of results to 

preferences regarding potentially competing environmental and economic goals. 

Steps for Conducting Simulation Optimization 

Step 1 Enter all factors (inputs, outputs, weights, constraints, etc.), 

Step 2 Define all processes (relationships among factors) 

Step 3 Identify which factors are uncertain and their expected range and 

probability distributions. 

Step 4 Identify the target cell to be maximized 

• Weighted sum of our four benefit indicators.

Step 5 Identify adjustable cells (control variables): 

• Weights on each benefit indicator (defined by the user) 

• Treatment intensity at each area (solved by the program) 

Step 6 Identify constraints

• “Hard” – budget 

• “Soft” – policy choices that limit the optimization 

Step 7 Assign a weight to each benefit (user preferences) 

Step 8 Run the program and assess results 

Step 9 Perform sensitivity tests on assumptions, weights, etc. 

Step 10 Interpret results and develop recommendations 
86 

 Initially, the optimization model specified to address this problem involved 

choosing one of five treatment intensities (including no treatment) to apply at each of 114 

potential treatment sites, a problem with many trillion potential "optimal" solutions 

(actual number = 4.81 X 1079). After an initial screening of options to exclude those that 

were clearly inferior in terms of minimizing costs or maximizing any specific 

environmental or economic objectives (based on very small fire size), the number of 

potential sites was reduced to 68. This screening reduced the number of potential 

"optimal" solutions, but the number remained in the trillions. Clearly this represents too 

many options to be compared in terms of expected costs and environmental and 

economic benefits without resorting to some kind of quantitative optimization method. 

6.1.1 Quantitative Optimization Methods 

 Quantitative optimization methods are used routinely in commercial, industrial, 

and military applications to minimize costs or maximize performance in situations where 

objectives and options are too complex and/or too numerous to be assessed and compared 

in any other way (Optimization Online 2006). Such models are being used with 

increasing frequency to help prioritize and manage environmental conservation and 

restoration initiatives (Aravossis et al. 2006). 

 There are many different types of optimization methods (Troutman 2006, 

Papalambros and Wilde 2000, Nocedal and Wright 2006). They are usually categorized 

on the basis of whether they are: linear or non-linear, static or dynamic, constrained or 

unconstrained, and so on. The choice of the best optimization method depends on both 

the nature of the optimization problem being addressed and the availability of data to 

model the problem. 

6.1.2 Optimization Techniques 

The selection of the optimization method defines how the problem is 

characterized within a quantitative optimization program. Each optimization program, 

however, employs a particular optimization technique or algorithm for finding an optimal 

solution. These techniques can be very different and can yield very different optimal 

solutions. They fall into categories with names that reflect their general approach for 

finding the best option among many. These categories include hill climbing, ant colony, 

simplex, stochastic tunneling and particle swarm optimization techniques (Fox and 

Sengupta, 1969). Some techniques are based on what are called evolutionary algorithms, 

including the one used here, which is referred to as a "genetic algorithm" (Goldberg 

1989, Rawlins 1991). 

6.1.3 Genetic Algorithms 

 Genetic algorithms derive their name from the fact that they search for an optimal 

solution using the same kind of "survival of the fittest" simulations that were developed 

to trace and forecast the evolutionary development of biological populations. Using this 

approach, populations (options) are pitted against one another to determine which is the 

fittest (most optimal) with respect to certain desirable characteristics (objectives). 

Seemingly successful populations are then recombined, as in a mating process, and 
87 

experience mutations and random variations that allow them to "evolve" into better 

solutions if possible. Genetic algorithms have advantages over other optimization 

techniques when considering large complex problems because they are relatively simple 

to program and can be more efficient at finding global optima. However, there is no 

guarantee that such algorithms will identify the optimal solution. 

6.1.3.1 Applying Genetic Algorithms 

Genetic algorithms can be applied to an optimization problem if it has two specific 

characteristics: 

1. it must be possible to express the solution as a "string" of solution values, where a 

string is equivalent to a string of chromosomes in conventional genetics 

2. it must be possible to calculate a value for each string in order to compare them 

with one another (where value is the contribution to an objective and is equivalent 

to the contribution to "fitness" in conventional evolutionary biology) 

With the cheatgrass optimal restoration problem, we determined that these two conditions 

were met. The solution could be described as a "string" that consisted of the level of 

treatment effort applied to each of the treatment sites; and the value of each potential 

string could be measured in terms of the cumulative expected contribution of the string to 

a weighted sum of four benefit measures (our measure of fitness). The strings are 

equivalent to vectors of treatment choice. 

Illustration 

 The cheatgrass optimization problem can be addressed using a genetic algorithm 

because it involves finding a string (more typically called a vector outside of this 

application) that consists of a level of treatment at each potential treatment site that 

maximizes the cumulative value of the weighted set of benefit indicator changes for each 

site. Table 15 illustrates the strings associated with a situation where there are only three 

potential treatment sites and only three potential treatment intensities. 

Table 15. Illustration of Strings and Related Value Measures for Cheatgrass Optimization 

(3 Treatment Sites, 3 Levels of Treatment, 3 Benefit Measures) 

Combinations (Strings) of Potential Treatment Options 

The total benefit index for each string is the weighted sum of the individual 

benefit indicators associated with various outcomes (e.g., wildlife habitat improvement, 

livestock grazing improvements, or recreational benefits). Individual benefit indicators 

associated with each string will depend on site and landscape factors that determine the 

restorability of specific types of benefits at each site, the weights assigned to those 

benefits, and the intensity of treatment. (see Equation 1). 

Site 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 

X 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 

Y 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 

Z 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 
88 

 In this illustration, the total number of strings under consideration is 27. This is a 

far more manageable number than the trillions of strings under consideration in our actual 

cheatgrass case study. However, note that even in this limited illustration, examining the 

sensitivity of optimization results to changes in weights assigned to the three different 

measures of benefits that make up the cumulative "value measure" for each string could 

result in the need for thousands of program runs. 

 The next section deals with how the choice of an optimization program should 

also depend on the level of uncertainty about the values of critical parameters that link 

different treatment intensities at sites with different site conditions and landscape 

contexts to the various benefit measures. If the level of uncertainty regarding one or 

more parameters is significant, it may be beneficial to have their values selected from a 

probability distribution and generate a distribution of potential benefit estimates for each 

string rather than simply using average or typical parameter values to generate a single 

benefit measure for each string. If this approach is used, the number of program runs 

required to converge on an optimal solution, even in the limited illustration described 

above, could be in the hundreds of millions or billions. The number of iterations and the 

criteria for stopping the program from recombining and mutating solution values is 

determined by the user. 

6.1.4 Dealing with Uncertainty 

 Besides being influenced by the significant number of potential treatment 

locations and intensity of treatment options, the selection of an optimization method to 

address the cheatgrass problem needed to take account of significant uncertainty about 

many of the parameter values and relationships that determine the links between levels of 

treatment at particular sites and various indicators of expected benefits. Typical 

optimization methods, whichever searching technique they employ, generate "optimal" 

solutions based on average or typical parameter values provided by the user. When there 

is significant uncertainty about the value of these parameters, relying on average or 

typical values can lead to sub-optimal solutions. In these situations, it may be far better 

to rely on the results of optimization programs that deal explicitly with uncertainty. 

 Traditional optimization programs, such as Evolver or Excel's built in Solver, 

require users to provide specific values for the parameters used to characterize the 

optimization problem (Frontline Systems 2006, Hallogram Publishing 2006). Some of 

them allow limited "brute force" approaches to testing sensitivity of results by running 

the model, adjusting some parameters, running the model again, and observing changes 

in results. This approach does not address the full range of uncertainty that exists in 

many situations, can be enormously time consuming, and makes it difficult for users to 

incorporate what they know about the range of uncertainty about each parameter into the 

search for an optimal solution. Fortunately, several new-generation optimization 

programs have been developed that combine simulation with optimization in ways that 

allow uncertainty to be incorporated directly into the selection of an optimal solution 

(Hegazy 2003, Pichitlamken and Nelson 2002). 
89 

6.1.5 Selection of "RISKOptimizer" Software 

The particular optimization software that was selected for use in our research was 

RISKOptimizer (Palisades Corp. 2006), a program that combines genetic algorithm 

methods for optimization with Monte Carlo simulation to characterize uncertainty. This 

software is relatively easy to use since it is installed as an extension to Microsoft Excel 

spreadsheet software. 

For characterizing uncertainty, the user has the ability to use one of many 

probability distributions to express uncertainty about parameter values, and to allow 

stochastic selection of parameters rather than being restricted to using deterministic 

values. For example, instead of assigning a value of 20 to a cell, the user can specify a 

triangular distribution where the expected value of the parameter ranges from 10 to 30, 

with a mean value of 20. As the genetic algorithm develops and examines "strings" that 

may be solutions, it selects values of this uncertain parameter based on this probability 

distribution along with values of all other uncertain parameters based on the uncertainty 

specified for them. In effect, the program initially selects the most "fit" strings of 

solutions based on the most probable combinations of parameters, and then uses the 

information provided about the uncertainty of each parameter to randomly change 

solution values until the likely values of the solution based on all combinations of 

parameter values begins to emerge. 

6.2 Optimization Model Implementation 

The optimization model was configured in the RISKOptimizer software using the 

framework discussed throughout this report and summarized in the inset box. The 

objective function was set to maximize the total change in benefit indicators by adjusting 

the levels of the treatment intensity for each burned area. 6 Five treatment intensities 

(including no treatment) were possible and two constraints were used. 

 

6

 The default values for options controlling the behavior of the genetic algorithm were used: mutation rate, 

crossover rate, population size, random number seed, and sampling. We set the simulation stopping 

conditions to run 100 iterations before moving on to the next simulation. 
90 

To set up the decision, as one that paralleled that of the management agency, we 

used data for only one year, 2002. In that year, 114 fires were recorded on BLM lands 

within the Twin Falls District. We selected only the fires that burned one or more acres 

(excluding small fires) to ease computations and reflect likely management behavior. 

Then, we analyzed the necessary GIS data related to calculating benefits, costs and 

restorability and calculated risk-adjusted benefits and costs for the 68 burned areas that 

could be located in the GIS. Of these fires, four had been treated by BLM Twin Falls 

District in 2002. Other data indicated that a total of 8 fires had been treated by the 

district. However, some of these fires could not be matched to our spatial (GIS) database 

of fires and one fire was shown as having less than 1 acre area in the database we used 

for screening and was therefore screened out, although the treatment database showed 

higher acreage burned at this site. 

The model was subject to two hard constraints: 1) the overall budget was limited 

to $1 million (based roughly on budgets of the two rehabilitation programs described in 

Section 4.3.1.1), and the number of burned areas that could be treated could not exceed 

10. The constraint on treated sites was set up to reflect the limited equipment and time 

Restoration Optimization Model 

Objective 

Maximize the change in benefits of multiple ecosystem 

services subject to a given budget constraint

Control 

Variables 

k = treatment level (0-4), the level of preventative/ 

restorative treatment provided to burned area i 

w = weights assigned to benefits j 

Bt = i j wj (bij – bij ) 

 i = Location i 

 j = Benefit j (brecreational hunting, 

bforage production bproperty protection, bexistence values ) 

 t = 2-3 years following restoration 

with without 

Budget 

Constraint 

FC = Fixed Costs 

JCk = Journey (Travel) Cost, personnel and equipment 

JTi = Journey Time (hours) 

TCAik = Treatment Cost per Acre 

 Ai = area treated (acres) 

 k = treatment intensity 

Hard Constraint: Number of Treated Fires ≤10 sites 

Total Costs ≤ $1,000,000

TCik = k FC + JCk*JTi

 + TCAik*Ai

Other 

Constraints 
91 

available to respond to fires. An average of about 10 burned areas were treated under the 

BAR and ESR programs, within the BLM Twin Falls district per year, based on our 3-

year dataset. We tested the effect of the limit on fire sites treated by comparing results of 

optimization runs with and without the constraint, discussed below. 

The benefits framework and optimization software were set up so that users could 

easily change the weightings applied to different types of benefits. Such weights were 

meant to be based on the relative importance given to different agency goals and to 

reflect necessary trade-offs. We initially applied an equal weighting to all services, in 

keeping with stated agency practices, and tested the sensitivity of results to this weighting 

by assigning all weight to each service, in turn. 

6.3 Optimization Model Results and Discussion 

6.3.1 Optimization Simulation Results Were Consistent Among Runs 

We found almost complete consistency of results among optimization runs, 

leading us to conclude that the software performed well in defining the optimal choice 

set. Models were typically run for 20 hours (2-6 million simulations), by which time, 

model output showed that total benefits were improving by less than 1% between 

simulations. Although the choice of which sites to treat did not vary, we found treatment 

intensity levels varied somewhat across runs. Therefore, small differences in treatment 

intensity choices between model runs should not be viewed as significant differences. 

We tested the sensitivity of the outcome to initial conditions and found that, given 

sufficient run time (~8 hours), model results were not sensitive to initial conditions or 

RISKOptimizer run parameters. The option to use Monte Carlo techniques to allow 

uncertainty of model parameters to be evaluated did not change the choice sets. 

Model results showed consistent selection of certain treatments. The optimization 

typically resulted in the lowest intensity of treatment (aerial seeding only) being applied 

to the majority of sites selected for treatment. A modest number of sites were assigned 

the second level of treatment (seeding + chaining) and only a few small fires were 

assigned the most intensive drill-seeding treatment. The treatment involving herbicide, 

the third highest intensity, was never assigned. 

6.3.2 Constraint on Number of Sites Treated Changed Average Size of Sites 

Selected 

The constraint of treating 10 or fewer burned areas had a major effect on which 

sites were selected for treatment. When unlimited fires could be treated, the software 

chose to treat many fires, with a small average size (Figure 17, Table 16). With the 10-

site constraint, the average burned area size increased, but total costs and benefits 

remained about the same (Figure 18, Table 16). This was not a major surprise since the 

main factor controlling site selection within the optimization program was the costeffectiveness ratio, and both small and large burned areas can have similar costeffectiveness. However, we had expected the economies of scale built into the cost 
92 

model to make the larger fire sites more cost-effective and therefore be favored by the 

selection algorithm. 

Optimization results generated with and without the 10-site constraint (weighting 

all benefits equally) showed no difference in average costs and average cost-effectiveness 

for optimization runs that treated 33 vs. 10 fires. Therefore, we concluded that the 

economies of scale were relatively minor and that other factors dominated the selection 

of burned areas to treat. This was confirmed when we plotted cost-effectiveness vs. size 

(Figure 19). While the plot shows that economies of scale are evident across the full 

range of fire sizes (small to large), the relationship over the range of small to mid-size 

fires is weak. 

This constraint on maximum fires treated may have important implications for a 

regional strategy of cheatgrass control. Without the limitation on number of fires treated, 

the model selected many small fires to treat, probably reflecting a higher probability of 

success and higher potential benefits. However, benefits were not substantially greater 

when many small fires were treated, suggesting that more work is needed to evaluate 

trade-offs involved in treating many small fires. However, other research has shown that 

treating small infestations has a greater ability to control invasive spread (Moody and 

Mack 1988, Bangsund et al. 1996). Such work has shown greater effectiveness or costeffectiveness of treating small sites to contain an infestation. In work that may have 

relevance to a regional treatment strategy, Bangsund et al. (1996) found an inverse 

relationship between leafy spurge infestation size and treatment payoff to ranchers when 

resilience of rangelands was considered. 

Table 16. Comparison of Solution Sets without and with Limit on Number of Sites Treated 

No Limit on Fires Treated Treatment limited to 10 fires 

Treatment Intensity 

Number Fires 

per treatment 

level 

Average Fire 

Size (acres) 

Number Fires 

per treatment 

level 

Average Fire 

Size (acres) 

No Treatment 33 1,696 58 1,071 

Aerial seeding only 19 3,138 6 7,194 

Aerial seeding and chaining 3 17 3 3,179 

Aerial seeding, chaining & herbicide 4 2 0 NA 

Aerial seeding, chaining & drill-seeding 9 13 1 964 
93 

Figure 17. Optimization Model Solution with No Limit on Treated Fires, Equal Weight on All 

Benefit Categories) 

Burned areas selected for rehabilitation by the optimization software are shown as colored dots. 

Black dots represented unselected sites. Dot radius represents relative fire size. 

Figure 18. Agency Choices vs. Optimization Results with 10-Site Limit, Equal Weight on All 

Benefits) 

Burned areas selected for rehabilitation by the optimization software are shown as colored dots. 

Black dots represent unselected sites. Burned areas treated by BLM in 2002 are circled in blue. 

(Only burned areas greater than 1 acre are shown. Not all sites treated by BLM are shown due to 

data limitations). 
94 

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000 20,000

Fire size (acres)

Cost-effectiveness (benefits/costs)

Figure 19. Cost-Effectiveness vs. Fire Size 

Some economies of scale are evident since this graph shows a positive relationship between costeffectiveness ratio and fire size. However, note that the few large fires drive the relationship and 

the economies of scale over the range of small to mid-size fires is weak. 

6.3.3 Benefit Category Weightings Affected Site Selection and Overall Change in 

Benefit Indicators 

The sensitivity of results (choices of sites and treatment intensities) to benefit 

category weightings was tested by conducting model simulations in which all weight was 

assigned sequentially to each of the four service ecosystem services. The results showed 

that the total change in benefit indicators was somewhat lower when forage production or 

property protection benefits were being maximized (Table 17). The specific site and 

treatment options selected did vary with different weighting schemes, as discussed in the 

next section. 

6.3.4 Benefit Category Weightings Did Not Affect Proportion of Benefits by 

Service Category 

Despite different weightings on benefit categories, the proportion of total benefits 

(as measured by change in indicator scores) achieved for any given benefit category did 

not differ substantially when weights were manipulated (Figure 20, Table 18). The 

relative proportion of total benefits realized in each of the four benefit categories 

remained roughly the same, regardless of which service benefit was being maximized. 

This result indicated that levels of benefits were highly correlated among the best site-
95 

treatment options. The bulk of the benefits, in all cases, were generated from existence 

values for sage-grouse and from recreational hunting benefits. The smallest proportion of 

benefits was derived from property protection. 

6.3.4.1 Model Structure Strongly Influenced Ability to Produce Multiple Ecosystem 

Services at Sites 

Before reviewing results of changes in benefit indicators in depth, it is important 

to clarify that aspects of the optimization model structure had the effect of minimizing the 

potential conflicts between some services. In particular, potential conflicts between 

forage production and services dependent on native habitat creation were minimized as a 

result of modeling choices. Conflict was minimized because of a simplifying assumption 

made regarding post-treatment vegetation cover. The change in benefits with treatment 

was based on the reduction in invasive species cover without specifying whether native 

grasses and shrubs were restored or whether non-native grasses were restored. In 

practice, conflict existed in this choice because native shrubs may be lower quality forage 

compared to non-native grasses that were commonly used in rehabilitation. Yet, sagegrouse existence benefits and antelope hunting benefits depended on the presence of 

shrubs. 

Although failing to specify vegetation outcomes would seem to be a critical 

omission, it was difficult to avoid given available data and information. A mix of native 

and non-native species was typically used by this management agency, with the 

proportion of native seeds determined by initial site conditions. Sites with higher 

probabilities of success were given higher proportions of native seeds, up to 100%. 

However, native seeds had a much lower probability of successfully germinating. As a 

result, the ability to predict details of vegetation outcomes of restoration and understand 

the relative effects on benefits was limited. 

With this model, we were able to distinguish the relative benefits derived from 

sites that differed in their likelihoods of successful treatment, as defined by preventing 

domination by cheatgrass. However, we were not able to model benefit indicator 

response to different mixes of native vs. non-native plants. To improve the model, 

information would be needed on the probability of different proportions of native vs. 

seeded non-native species establishing in response to different treatments. In addition 

information on how each service would respond to those different proportions of 

vegetation would also be needed, something we were not able to establish quantitatively. 

Therefore, our model structure glosses over some conflicts related to the specific 

vegetation established. In particular, the use of crested wheatgrass has been suggested to 

generate some ecological harms that we did not try to capture (Keeley 2004). Future 

efforts should endeavor to close this information gap since it is vital to understanding 

how services may compete when restoring sites. 
Table 17. Optimization Solution Sets Summary for Different Ecosystem Service Weightings 

Treatments Selected 

No Treatment 

Aerial seeding 

only 

Aerial seeding 

and chaining 

Aerial se

chainin

herbic

Optimization Program Maximizing: 

Total 

Change in 

RiskAdjusted 

Benefits 

Total 

Cost 

# 

fires 

Average 

fire size 

# 

fires 

Average 

fire size 

# 

fires 

Average 

fire size 

# 

fires 

Av

fir

All service categories equal 2,834,436 $999,969 58 1,071 6 7,193 3 3,179 0 Recreational Hunting only 2,830,018 $996,835 58 1,072 6 7,194 2 4,733 0 Forage Production only 2,670,331 $998,772 58 1,116 6 5,828 4 4,015 0 Property Protection only 2,554,258 $998,087 58 947 8 6,718 2 3,550 0 Existence Values only 2,885,233 $998,376 58 970 7 7,647 3 1,990 0 
97 

Table 18. Distribution of Benefits among Ecosystem Services when Service Weights Varied 

Total Change in Benefits from Optimization Program Run 

Benefit Maximized 

Recreational 

Antelope Hunting 

Forage 

Production 

Property 

Protection 

Existence Values 

for Sage-Grouse 

All service categories equal 536,311 723,971 11,546 1,562,608 

Recreational Hunting only 534,328 722,401 11,520 1,561,768 

Forage Production only 463,879 777,673 9,180 1,419,599 

Property Protection only 477,481 642,929 13,137 1,420,711 

Existence Values only 522,091 724,743 11,596 1,626,803 

Distribution of Total Benefits when Recreational Hunting Benefits 

Maximized

Recreational Antelope Hunting

Forage Production

Property Protection 

Existence Values for Sage-Grouse

Figure 20. Typical Distribution of Benefits among Service Categories in Optimization 

Model Results 

Figure shows resulting allocation of benefits among ecosystem service categories when all weight 

was given to Recreational Hunting in optimization model. This chart is representative of all 

model runs since the proportions of benefits by category varied only slightly for different benefit 

indicator weighting schemes.

6.3.4.2 Model Structure Influenced Proportions of Benefits Derived from Different 

Ecosystem Services 

Several factors drove the relative proportion of the increases in ecosystem 

services. A primary factor was the scaling used to adjust service categories. Our scaling 

method assigned the maximum value of 100 to the highest score on the landscape and 

normalized all other values to that maximum value. This scaling method was sensitive to 

the shape of the distribution of benefit indicator values. The more consistent or even the 

raw scores were over the range of potential values, the greater the number of sites with 

high scores. Conversely, the more skewed the distribution towards high values, the fewer 
98 

the sites that scored well. In the case of property protection, one fire was near an urban 

area, while the majority of sites were in remote locations. The urban site had the largest 

potential user population of fire protection services with 15,260 people within a 3-mile 

radius, whereas the mean score for all other sites was 252 people within the 3-mile 

radius. Therefore, when the maximum score of 100 was assigned to that urban location, 

which was an extreme outlier in the distribution, other sites were given proportionately 

low scores. 

This result demonstrates how seemingly simple scaling rules can have a major 

influence on model results and may bias scores in unintended ways. In this case, we were 

not troubled by the model assigning a low score for remote sites for the benefit of 

property protection, since it accurately reflected the relative importance of preventing fire 

in an urban area vs. a remote area. However, managers should ensure that scoring rules 

match their priorities. Managers may want to score sites consistently across regions 

rather than just scaling values to the data at hand. This sensitivity to data distribution can 

be minimized by adopting alternative scaling rules or data transformations. However, all 

scaling choices reflect subjective choices that should be matched to management goals. 

In addition to scaling, another factor that altered the relative responsiveness of 

benefits to treatment was the m parameter used in the equation relating benefits to change 

in native cover (Equation 4). Habitat was given the smallest m value, meaning it 

increased more slowly than other benefits as native cover increased. As a result, it did 

not level off as quickly as other benefits, making habitat more sensitive to changes in the 

ranges we were evaluating (80-95% native cover, see Figure 3). Conversely, the slope of 

forage production was small over the 80-90% range of native cover since the steep part of 

this response occurred at much lower levels of native vegetation. Unfortunately, this 

demonstrated that our results were quite sensitive to a parameter for which we had 

limited information. 
99 

6.3.4.3 Level of Service Varied Spatially 

Under different service weightings, the spatial patterns of treated sites differed 

noticeably between simulation runs (Figures 21 a-d) indicating that services were 

spatially heterogenous across the region. The sites chosen when habitat benefits were 

maximized included some more remote sites in the NW part of the region (Figure 21a). 

Whereas, when property protection benefits were maximized, the burned area in the SE 

that had been treated by the management agency was selected. However, some sites were 

common to all sets, despite different weightings on service benefit categories. 

6.3.5 Agency Optimized Individual Services per Site While Optimization Model 

Optimized Multiple Services per Site 

The comparison of optimization model results and agency choices demonstrated 

that more agency-treated sites were chosen (as part of multiple optimal sets) when full 

weight was assigned to a single service, than when all services were weighted equally. 

These results suggested that managers were choosing sites that produced the highest 

benefits for individual services and not evaluating the sites as producers of multiple 

Compromise Programming Framework for Scaling Benefit Indicators 

Many alternative systems for scaling indicators exist. A class of scoring rules 

used in Compromise Programming (Zeleny 1973) creates scaling rules that can be 

used to quality-adjust the change in benefit indicators, such that changes in an 

indicator are evaluated in terms of the perceived benefits they produce. For example, 

changes of the same magnitude but at different points in the range of possible scores 

can be treated differently when they result in different levels of improvement. A net 

change of say 20 points, when it occurs close to an ideal score (e.g., moving from 80 

to 100) might be given a larger weight than the same 20-point change when it occurs 

in a degraded site (e.g., a movement from 20 to 40). For our indicator scoring system, 

we did not explicitly weight the change in benefits in such a manner, rather, we used 

supplemental variables (landscape context Ci and restorability) to reflect the quality or 

importance of a change in a benefit index. 

In a compromise programming framework, indicators are judged using ideal 

and anti-ideal sites. A change in benefit index score would be evaluated in terms of 

the distance a site moves towards an ideal site, measured in indicator state space, 

divided by the potential distance between the ideal and anti-ideal sites within the 

landscape. In other words, the deviation from the ideal is calculated as a percent of 

the total deviation observed in the landscape. 

The advantages of such a system are that scores can be made consistent across 

sets of sites being evaluated and made consistent with management goals. In addition, 

by choosing an ideal site within the landscape being managed, goals are realistic with 

respect to limitations created by the landscape. A major disadvantage is that the ideal 

site may not be easy to identify or may not represent diverse viewpoints. 
100 

services. Whether benefits could have been produced simultaneously at sites deserves 

further review since it was unclear whether current treatment practices result in services 

being generated simultaneously on sites. However, if benefits are not in conflict at some 

sites, our results suggest managers may be missing an opportunity to maximize benefits 

of spending by failing to choose sites that produce multiple services simultaneously. 

The sole agency-treated site that was not selected by the optimization model 

either represented a problem with our data or model, or an opportunity to improve 

decisions. We suspected that some sites chosen by the agency might not fully reflect all 

costs or risks associated with sites, and this result bears that out. The treated site that was 

never selected for treatment in the optimization software scored high in terms of available 

benefits after treatment, but our data suggested that the site was in a location where it had 

a high likelihood to recover on its own. Therefore, the change in benefits with treatment, 

for this isolated site, would be negligible. However, our data on cheatgrass coverage and 

recoverability is admittedly weak. Therefore, further information would be needed to 

evaluate whether this decision to treat was inefficient, as the model results suggested, or 

whether it reflected knowledge not captured in the model. 
Figure 21a. Hunting benefits only. Figure 21c. Property protection benefits only. 

Figure 21b. Forage production benefits onlyFigure 21d. Sage-grouse habitat benefits on

Figure 21 a-d. Maps of Solution Sets from Optimization Model and Agency Choices in 2002 Colored dots represent model output; dot size represents fire size. Each map shows results when the specified benefit ca

full weight. Four of the agency selected sites are shown circled in blue. Note that all but one agency-treated site (the sou

circle) was chosen in one or more model solution sets. Not all agency-treated sites could be evaluated due to data limitat

N
102 

6.3.6 Optimization Results vs. Agency Selections: Model Generated Higher 

Benefits by Selecting Options that Produced Multiple Services 

A major question we addressed was, “Did the optimization model produce results 

different from those of the management agency?” We expected similar results for three 

reasons: 1) we constructed much of the benefits assessment framework to reflect 

manager conceptions of important environmental services produced on the landscape. 

2) we used management opinions about restorability to inform our risk-weighting of 

benefits and 3) we used constraints that reflected those of the management agency. 

On the other hand, we had reason to expect our results would differ for several 

reasons. First, we were not certain that managers, in their decisions, had captured the 

indirect costs of treating sites, such as those incurred in travel to sites and supervising 

contractors. We were able to include part of, but not all of, those costs in our model. 

Second, we used a maximum of 10 treated sites, which was slightly higher than the five 

mapped fires observed to have been treated in the year we compared.7

 Finally, we were 

not certain that the GIS data were adequately reflecting the detailed site-based 

information available to managers. For these reasons, we expected our results might 

deviate from management choices. 

In a plot of benefits vs. costs, we identified that the choice sets of the optimization 

model and the management agency were not dramatically different in their costeffectiveness (Figure 22). For both the optimization model and the agency, the selected 

sites generally fell close to or on the cost-efficient frontier. However, one point chosen 

by the management agency shows apparently low benefits for modest costs and is far 

from the efficient frontier. For the optimization model, points chosen that were close to 

but off of the efficient frontier appeared to reflect trade-offs made by the software to 

maximize benefits without exceeding the budget although it is also possible the software 

did not identify the most optimal set. 

 

7

 We ran the optimization with a constraint of a maximum of 5 sites and found that the 5 sites selected were 

consistently captured within the set of 10 sites selected under the 10-site constraint. This result indicated 

that even if the agency were required to choose fewer sites, those sites should have been included in the set 

of 10 sites. 
103 

0

200,000

400,000

600,000

800,000

1,000,000

1,200,000

1,400,000

$0 $100,000 $200,000 $300,000 $400,000 $500,000 $600,000 $700,000

Costs

Benefits

All options

Optimized options

Agency-selected options

Figure 22. Risk-Weighted Benefits vs. Costs of Model and Agency Selected Options 

The most cost-efficient sites are those along the cost-efficient frontier (dashed line). Sites in the 

bottom left are low cost–low benefits while sites in the upper left are low cost–high benefit. 

When we compared the change in benefit indicators for the four agency-selected 

sites for which we had data and the top five sites chosen by the model, we found that the 

total benefits were substantially higher for the optimization model set than for the agency 

set. Such results should be viewed with caution due to the potential for inaccuracies of 

our model or the inability of the landscape data and screening-level analysis to capture 

the site-based information available to the agency. However, these results, and the results 

discussed in the previous section, suggest that the agency may be able to generate higher 

levels of ecosystem services through their restoration choices by selecting sites that can 

provide multiple services well, compared to selecting sites that provide a particular 

service well. 
104 

Figure 23. Comparison of Per Acre Benefits for Options Selected by Optimization Model 

and Agency 

Bar graphs show the change in the bundles of ecosystem services produced by sites as a result of 

the selected treatment. The change in benefit indicators for each site is shown as the per-acre 

change in indicators to remove the effect of fire size. Note that all but one of the sites chosen 

with the optimization model generated substantial benefits across all categories of service while 

benefits of agency selections are more likely to be concentrated in a single service. Site D in the 

left side graph and site Y in the right-side graph are the same site. At least one burned area 

treated by the agency was not able to be represented by available data, so this graph does not 

show all fires treated by the agency. 

6.3.7 Caveats on Scope of Analysis 

Through this analysis that focused on site and neighborhood-based costeffectiveness, we did not examine some of the regional trade-offs inherent in site 

selection. Our model constraints led the model to choose large rather than small fires, but 

this binding constraint needs to be examined further to determine how it fits into a 

strategy of regional control of cheatgrass. We did not explicitly examine how different 

types of preventative treatments in unburned areas might be used in a strategy to 

manipulate fire regimes (e.g., by creating regional fire breaks) and thereby create similar 

types of benefits to direct rehabilitation of burned areas. Also, we did not consider the 

potential harms of treatment, which are just beginning to be understood. These risks 

include the potential for treatment to facilitate invasion by even more harmful species 

than cheatgrass (Keeley 2006). In addition, we did not examine trade-offs having to do 

with the use of alternative methods of risk reduction such as providing incentives for 

homeowners to build in different locations or with different materials. Such issues are 

important to identifying optimal solutions for how to allocate funds among programs but 

are typically beyond the scope of analyses conducted by management agencies. 

Optimization Model Selected Options

0

10

20

30

40

50

60

70

80

90

100

ABCDE

Site

Habitat/ Existence

Property Protection

Grazing 

Hunting/ Recreation 

Agency Selected Options

0

10

20

30

40

50

60

70

80

90

100

WX Y Z

Site

Habitat/ Existence

Property Protection

Grazing 

Hunting/ Recreation 
105 

6.3.8 How Does Scale of Analysis Affect Perceived Benefits? 

Because benefits of different services accrue to different sets of users, benefit 

weights attach relative importance to different scales of analysis. Through our analysis 

methods for devising indicators to measure relative benefits, we effectively assigned a 

representative scale of user benefits. We were interested to see whether total benefits 

differed when the scale of services being weighted changed. Specifically, forage 

production benefits were evaluated in terms of site qualities only, and thus relative 

benefits were measured at the plot scale. These forage-production benefits would be 

realized primarily by the lease-holder. Next in increasing scale, was the property 

protection service which benefited a relatively small area of nearby residential 

landowners (3-mile radius). At a broader scale, hunting benefits applied to a potential 

user group within a 1.5-hour drive (~75 miles). 

For existence values, we did not have an indicator that explicitly identified the 

human population receiving benefits. Rather, we developed the index to reflect qualities 

of the landscape that were important to sage-grouse, intending that factors supported 

long-term sage-grouse survival would reflect the relative benefits to those who value 

sage-grouse. Sage-grouse are not just affected by site conditions, but also the landscape 

context in which sites exist. Therefore, the landscape indicators were used to assess 

aspects of habitat quality over a 10,000 hectare area surrounding each burned area. 

However, implicit in our indicator selection was the concept that the location of the 

existence service did not affect the values people hold for that service, as long as habitat 

quality was held constant. Since the service was defined as a non-use service, we did not 

need to weight the service by accessibility by people. 

Although an existence (non-use) service should imply that all sage-grouse 

populations are substitutable, we did not think the beneficiaries within the management 

area would agree. Conceptually, we envisioned the user group as being the affected 

population within the management district, since maintaining this characteristic species 

locally was a clear goal of the local management agency. Other populations of sagegrouse throughout the Intermountain West may be substitutes for beneficiaries outside 

the region. Therefore, the main beneficiaries of this service were the local residents, at 

least until the population of sage-grouse becomes sufficiently rare that all habitat is seen 

as critical to its survival. 

By revisiting the optimization results generated when different service weights 

were applied, we can see that scale of analysis did have an effect on which sites were 

chosen for treatment and the relative level of benefits, as measured by our system of 

benefit indicators. Sites that maximized forage production benefits (site scale) were 

different from sites that maximized property protection or hunting benefits. However, 

sets had some overlap regardless of which service benefit was being maximized, 

suggesting scale of analysis would affect treatment priorities to some degree. As would 

be expected, the benefits were seen to increase as more services (increasing scales) were 

included in the analysis. 
106 

7. Conclusions 

Our goals with this project were to 1) demonstrate how economic principles could 

be incorporated into an indicator-based framework used for assessing and comparing the 

social benefits of invasive species treatment alternatives; 2) evaluate whether and how 

optimal treatment decisions would differ as benefits of different ecosystem services were 

given different weight; 3) evaluate effects on treatment decisions of explicitly accounting 

for spatial heterogeneity of costs, benefits, and risks; 4) evaluate whether existing data 

and knowledge were adequate to create practical quantitative decision tools; and 5) assess 

the potential usefulness to managers of modern quantitative optimization techniques for 

choosing optimal sets of treatment options. In developing these tools, the overarching 

goal was to keep methods accessible to managers and to fit economic tools to current 

decision support tools, such as GIS databases and analysis, in order to encourage the use 

of economic concepts in decisions made by non-economists. The incorporation of 

economic principles, even imperfectly, has the potential to generate recommended 

treatment regimes that compare favorably with or perhaps improve upon ad hoc 

decisions. 

We used a case study of one of the best studied invasive species in North 

America, cheatgrass (Bromus tectorum). After reviewing much of the available 

information about this species, we developed models to: 1) measure indicators of relative 

social benefits for four ecosystem services by location, 2) estimate treatment costs by 

location, and 3) estimate restorability of ecosystem services by location. Then we 

combined our site-specific measures of costs, benefits, and restorability within an 

optimization framework to generate optimal sets of treated areas and treatment intensities 

that maximized a weighted sum of social benefit subject to a fixed budget constraint. 

We worked closely with management partners from federal agencies to capture 

their knowledge about the problem and to incorporate their treatment goals into our 

analysis framework. We further informed the optimization framework with the best 

available research and data, although we found that even for cheatgrass, one of the moststudied invasives in the United States, a great deal of information was lacking. As a 

result, the model relied more heavily on ecological and economic first principles and best 

professional judgment of managers, scientists and our research team than was initially 

planned. This suggests that until databases improve, developers of decision-support 

models for less-studied invasive species should probably focus as much attention on 

methods of eliciting parameter and indicator values from experts as finding them in the 

literature or estimating them from data. 

7.1 Management Implications 

Despite the many concerns and caveats we raised on the difficulty of developing 

an objective evaluation of benefits, costs and risks, the screening method we developed, 

based on the best information available, was able to largely replicate choices made by 

managers who had detailed site-based information. This result suggests that current data 

and knowledge are sufficient to capture the decision process in a standardized framework 

that can be opened up to public and scientific input. Since we were not able to base the 
107 

framework on completely objective information, it seems particularly important that the 

approach we developed reveals the underlying assumptions, values and tradeoffs 

associated with agency decisions and enables researchers and stakeholders to understand 

how their input can and is being used. 

A major distinction between the results of the optimization model and the agency 

choices was that when we gave benefit categories equal weight, in keeping with stated 

agency practices, the selected set had only one treatment site in common with the agencyselected set of sites. However, when we gave full weight to individual benefits 

sequentially, and compared all optimization model selections to agency selections, all but 

one site was common to both sets. This indicated that managers picked sites to treat by 

choosing those that maximized a particular service benefit (e.g., the best habitat site, the 

best property protection site) rather than choosing sites that jointly produced high levels 

of multiple services. Because the agency selected a different set of sites than the 

optimization model, when all benefits were weighted equally, our model suggests there is 

an opportunity cost of choosing sites as producers of individual services rather than as 

producers of joint services. 

Some questions remain regarding the ability of services to be simultaneously 

provided at all sites. Several simplifying assumptions we made in our analysis 

framework to accommodate data constraints, may have minimized the potential conflict 

between forage production and sage-grouse habitat or antelope hunting services. The 

agency choices could be more accurately reflecting conflicts that our framework was not 

able to reveal. However, even if only some sites can be managed to produce multiple 

services, our results suggest it may be possible to generate a higher level of benefits by 

considering joint production of ecosystem services where they can be achieved. 
108 

7.1.1 Summary of Lessons Learned: 

4. The ecosystem service benefits generated from treating cheatgrass might be 

improved by viewing sites as simultaneous producers of multiple services rather 

than selecting sites that maximize only one service benefit. 

5. Analysis details are important and relevant to managers, so a screening analysis 

must incorporate at least an intermediate level of detail to be acceptable to 

managers, but also must make simplifying assumptions to remain tractable. 

6. Benefit response functions to invasive species are not well documented; but 

screening-level economic analysis based on first principles of ecology and 

economics can duplicate analyses based on site-specific information 

7. Data are sufficient to perform screening level analysis, but results are sensitive to 

the functional form of benefits, which is not well-constrained 

8. Weights on benefits are only critical when benefits compete; when they do, 

weights can significantly change the optimal allocation of treatment effort and 

treatment intensities 

9. Decision-support tools that follow sound economic principles and reveal 

underlying assumptions and value judgments provide a basis for both expert and 

stakeholder involvement in decision-making and promote cost- and risk-conscious 

solutions 

7.1.2 Use of Cost-effectiveness Analysis and Optimization Models 

The practical use of optimization models to select high priority preservation or 

restoration areas is a hotly debated topic because such models typically have difficulty 

capturing the real-life constraints of manager’s decision problem (Drechsler 2005). A 

significant problem, in the case of static models, is that the dynamics of making 

selections are ignored. In other words, once an area has been selected for restoration, the 

goals for and potential benefits of making other selections change. However, a static 

model cannot incorporate these dynamics. More complex dynamic models have the 

potential to overcome this problem, but they also present significant data and analytical 

challenges and frequently some level of detail must be forfeited when developing a 

dynamic model. 

The benefits of using a cost-effectiveness and optimization framework are that 

even when the models rely in part on best professional judgment, they expose 

assumptions, reveal the influence of different assumptions, and allow competing 

assumptions to be compared on the basis of various benefit measures, cost-effectiveness, 

or some combination. The drawbacks are that it is difficult to support the generalizations 

needed to allow many sites to be screened. 

In our attempts to build a decision support framework with an intermediate level 

of complexity, we quickly found that we could not find enough hard evidence to support 

our intended simplifications. It was our conclusion that the goal of creating a screening 
109 

tool to assist managers and potentially increase the benefits that can be derived from 

restoration programs is severely hindered by the lack of relationships to characterize 

system response to change. Even with all the simplifying assumptions we made, the 

decision support tool we eventually developed turned into a fairly complicated evaluation 

technique based on many weakly supported assumptions. This reflects both the messy 

nature of natural resource decisions and the poor quality of information available to 

characterize how people derive benefits from natural assets. 

Clearly, much work remains to specify functional relationships that represent 

change in ecosystem service levels as a function of invasive cover that are also tailored to 

specific services. We used a stylized relationship to suggest a likely relationship, 

however, the functions do not represent quantitative relationships developed from 

observed relationships. We may never be able to achieve such an ideal for these 

relationships given the complex nature of ecosystems. In which case, we should continue 

to test the sensitivity of our management choices to our assumptions of such 

relationships. 

Our framework appears to have succeeding in representing most of the factors 

that managers consider when setting restoration priorities. In this way, our framework 

can be used to focus public debate over how public lands are managed and can make it 

easier to incorporate new input on the scientific and economic basis of such decisions. 

Agencies that are struggling with such decisions may find the experiences described here, 

with respect to cheatgrass in our study area, to be helpful for informing their choices. 

The research described in this report demonstrated that it is possible to develop 

useful decision support tools to help assess and compare invasive species treatment 

options. However, it also demonstrated the difficulties inherent in making prioritization 

decisions in this area, and the difficulties of capturing the multi-faceted aspects of social 

value and their ecosystem linkages in a single quantitative decision-support framework. 

To develop models that are more rigorous and generate more credible results, future 

efforts of this kind will need to be well-supported so that managers and decision support 

tool developers have the time to review existing scientific information together, elicit best 

professional judgment, and create decision-support models that match the level of 

knowledge and amount of data that are available. The plans of BLM and USGS to 

improve invasive species monitoring databases will greatly increase the tractability of 

creating these types of decision-support frameworks. However, we still have a long way 

to go before we will have the capacity to capture, test, and properly interpret the 

accumulated knowledge about particular invasive species problems, and to then 

incorporate them into a reliable and generally applicable decision support tool. 
110 

7.2 Recommendations for Further Study 

7.2.1 Ecological Information Required to Improve Risk Analysis 

Improve analysis of enhanced risk of fire due to cheatgrass/ annual grass cover 

(see work by D. Pyke and others) 

Continue research to establish efficacy of treatments by evaluating sites in a range 

of environmental conditions (see work by N. Shaw and others) 

Evaluate whether treatments provide opportunities for new invasives to establish 

Untreated control sites should be monitored long-term to evaluate natural 

recoverability and establish dynamics of multiple invasive species 

Develop spatial time-series data of cheatgrass cover to allow better risk analysis 

and improve regional strategic planning 

7.2.2 Economic Research Needs 

Although we demonstrated that a static analyses can incorporate concepts of 

benefit persistence, further research is needed to develop methods that adjust 

benefit measures to changing regional losses of ecosystem services 

Dynamic models are required to directly assess the value of increasing fire-free 

interval as a result of cheatgrass treatment 
111 

8. References 

Anselin, L. and R.J. Florax, 1995. New Directions in Spatial Econometrics. New 

York:Springer Verlag. 

Aravossis, K., C.A. Brebbia, E. Kakaras, and A.G. Kungolos, 2006. Environmental 

Economics and Investment Analysis. Southampton, England: WIT Press. 

Babcock, B. A., P. G. Lakshminarayan; J. Wu; D. Zilberman, 1997. Targeting Tools for 

the Purchase of Environmental Amenities. Land Economics, 73(3):325-339. 

Bangsund, D.A., J.A. Leitch and F.L. Leistritz, 1996. Economics of herbicide control of 

Leafy Spurge (Euphorbia esula L.). Journal of Agricultural and Resource 

Economics 21(2): 381-395. 

Bartlett, E.A., S.J. Novak, and R.N. Mack, 2002. Genetic variation in Bromus tectorum

(Poaceae): differentiation in eastern United States. American Journal of Botany 89: 

626-636. 

Bell, K. P. and N. E. Bockstael, 2000. Applying the generalized-moments estimation 

approach to spatial problems involving microlevel data. The Review of Economics 

and Statistics 82(1):72-82. 

BirdLife International 2005. Species factsheet: Alectoris chukar. Downloaded from 

http://www.birdlife.org on March 20, 2005. 

BirdLife International 2006. Species factsheet: Centrocercus urophasianus. Downloaded 

from http://www.birdlife.org on July 20, 2006. 

Bockstael, N.E., 1996. Modeling economics and ecology: The importance of a spatial 

perspective. Am. J. Agr. Econ. 78, 1168–1180.

Bockstael, N.E., W.M. Hanemann and C.L. Kling, 1987. Modeling recreational demand 

in a multiple site framework. Water Resources Research 23: 951-960. 

Bockstael, N.E., K.E. McConnell and I.E. Strand. 1989. Measuring the Benefits of 

Improvements in Water Quality: The Chesapeake Bay. Marine Resource 

Economics 6:1-18. 

Bohlen, C. and D. King, 1995. The cost of wetland creation and restoration. Final 

Report to Department of Energy, Bartlesville Project Office, Oklahoma. 

DOE/MT/92006-9. 

Bowker, J.M.; Murphy, D.; Cordell, H.K.; English, D.B.K.; Bergstrom, J.C.; Starbuck, 

C.M.; Betz, C.J.; Green, G.T., 2006. Wilderness and primitive area recreation 

participation and consumption: an examination of demographic and spatial factors. 

Journal of Agricultural and Applied Economics, 38(2):317-326. 

Boyce, M.S., 1992. Population viability analysis. Annual Review of Ecology and 

Systematics 23: 481–506. 

Boyd, J. and L.A. Wainger, 2002. Landscape indicators of ecosystem service benefits. 

American Journal of Agricultural Economics 84(5): 1371-1378. 
112 

Boyd, J. and L.A. Wainger, 2003. Measuring Ecosystem Service Benefits: The Use of 

Landscape Analysis to Evaluate Environmental Trades and Compensation. 

Resources for the Future, Discussion Paper 02-63. 

http://www.rff.org/disc_papers/PDF_files/0263.pdf 

Bradley, B. A. and J. F. Mustard, 2005. Identifying land cover variability distinct from 

land cover change: Cheatgrass in the Great Basin. Remote Sensing of Environment 

94 (2005) 204–213. 

Brooks, M.L., C.M. D’Antonio, D.M. Richardson, J.B. Grace, J.E. Kelley, J.M. 

DiTomaso, R.J. Hobbs, M. Pellant, and D. Pyke, 2004. Effects of invasive alien 

plants on fire regimes. BioScience 54: 677-688. 

Brooks, R.P., D.H. Wardrop and C.A. Cole, 2006. Inventorying and monitoring wetland 

condition and restoration potential on a watershed basis with examples from Spring 

Creek Watershed, Pennsylvania, USA. Environmental Management 38: 673-687. 

Brown, C.S. and H. I. Rowe, in press. The unwelcome arrival of Bromus tectorum to high 

elevations. Proceedings of the High Altitude Revegetation Workshop. March 3-5, 

2004, Fort Collins, Colorado. 

Bureau of Land Management, 2004. Website: http://www.firehistory.blm.gov. File used 

was “firehistory_1980_2003”, published on 9/21/2004. Data contact: David 

O'Rourke, National Science and Technology Center, Denver, CO. 

Bureau of Land Management (BLM), 2005. Draft Vegetation Treatments Using 

Herbicides on Bureau of Land Management Lands in 17 Western States 

Programmatic EIS (PEIS). Washington Office, Washington, DC. 

http://www.blm.gov/nhp/spotlight/VegEIS/ 

Conservation Biology Institute, 2005. Protected Areas Database ordered on CD from 

http://www.consbio.org 

Cordell, H.K., G.T. Green, V.R. Leeworthy, R. Stephens, M.J. Fly, and C.J. Betz, 2005. 

United States of America: outdoor recreation. In G. Cushman, A.J. Veal, J. Zuzanek 

(Eds.), Free time and leisure participation: international perspectives, pp. 245-264. 

Wallingford, Oxfordshire UK: CABI Publishing. 

Coulson, T., G.M. Mace, E. Hudson and H. Possingham, 2001. The use and abuse of 

population viability analysis. Trends in Ecology & Evolution 16(5): 219-221. 

Crandall, C., 1893. Colorado weeds. Colorado Agricultural Experiment Station Bull 23. 

Cressie, N.A.C., 1991. Statistics for Spatial data. New York: Wiley 

D’Antonio, C.M. and P.M. Vitousek, 1992. Biological invasions by exotic grasses, the 

grass/fire cycle, and global change. Annual Review of Ecology, Evolution and 

Systemics 23:63-87. 

Davison, Jason, 2005. personal communication. University of Nevada Cooperative 

Extension, Fallon Nevada 89406 

Daubenmire, R. F., 1968. Steppe vegetation of Washington. Washington Agricultural 

Experiment Station Tech Bull 60. 
113 

DellaSala, D.A., N.L. Staus, J.R. Strittholt, A. Hackman, and A. Iacobelli, 2001. An 

updated protected areas database for the United States and Canada. Natural Areas 

Journal, 21(2): 124-135. 

Denne, T., 1988. Economics of Nassella Tussock (Nassella trichotoma) control in New 

Zealand. Agriculture, Ecosystems and Environment 20: 259-278. 

DiTomaso, J.M. 2000. Invasive weeds in rangelands: Species, impacts and management. 

Weed Science. 48:255-265. 

Drechsler, M., 2005. Probabilistic approaches to scheduling reserve selection. 

Biological Conservation 122: 253-262. 

Duda, M.D., S. J. Bissell, K.C. Young, 1995. Factors Related to Hunting and Fishing 

Participation in the United States, Phase V: Final Report. Responsive Mangement 

Western Association of Fish and Wildlife Agencies. 

Dukes, J.S. and H.A. Mooney, 1999. Does global change increase the success of 

biological invaders? Trends in Ecology and Evolution 14(4): 135-139. 

Duncan, B.W. and P.A. Schmalzer, 2004. Anthropogenic influences on potential fire 

spread in a pyrogenic ecosystem of Florida, USA. Landscape Ecology 19: 153-165. 

Eiswerth, M.E. and JS. Shonkwiler, 2006. Examining post-wildfire reseeding on arid 

rangeland: a multivariate tobit modelling approach. Ecological Modelling 192:286-

298. 

English, D.B.K, C.J. Betz, M. Young, J.C. Bergstrom and H.K. Cordell, 1993. Regional 

Demand and Supply Projections for Outdoor Recreation. USDA Forest Service 

General Technical Report RM-230. Rocky Mountain Forest and Range Experiment 

Station. 

ESRI, 2005. Cost distance function, as described in ArcGIS Desktop Help, v. 9.1. 

Environmental Systems Research Institute, Inc. Redlands, CA. www.esri.com. 

Evans R.D., R. Rimer, L. Sperry, and J. Belnap, 2001. Exotic plant invasion alters 

nitrogen dynamics in an arid grassland. Ecological Applications 11(5): 1301-1310. 

Fahrig, L., 2003. Effects of habitat fragmentation on biodiversity. Annual Review of 

Ecology, Evolution, and Systematics 34: 487-515. 

Feather, P. and D. Hellerstein, 1997. Calibrating benefit function transfer to assess the 

conservation reserve program. American Journal of Agricultural Economics 79: 151-

162. 

Ferguson, Sue A.; McKay, Steven J.; Nagel, David E.; Piepho, Trent; Rorig, Miriam L.; 

Anderson, Casey; Kellogg, Lara., 2003. Assessing values of air quality and visibility 

at risk from wildland fires. Res. Pap. PNW-RP-550. Portland, OR: U.S. Department 

of Agriculture, Forest Service, Pacific Northwest Research Station. 59 p. 

Ferrier, S., R. L. Pressey, T W. Barrett, 2000. A new predictor of the irreplaceability of 

areas for achieving a conservation goal, its application to real-world planning, and a 

research agenda for further refinement. Biological Conservation 93:303-325 

Fortin, M.-J. and M.R.T. Dale, 2005. Spatial Analysis: A Guide for Ecologists. 

Cambridge. 380 pp. 
114 

Fox, K.A. and J.K. Sengupta, 1969. Economic analysis and operations research: 

optimization techniques in quantitative economic models. Amsterdam: NorthHolland Publishing Company. 

Frontline Systems, Inc.. Solver Software for Microsoft Excel. 

www.solver.com/exceluser.htm. Incline Village, NV. 

Gelbard, J.L. and J. Belnap, 2003. Roads as Conduits for Exotic Plant Invasions in a 

Semiarid Landscape. Conservation Biology. 17(2):420-432. 

Geoghegan, J., L.A.Wainger and N.E. Bockstael, 1997. Spatial landscape indices in a 

hedonic framework: an ecological economics analysis using GIS. Ecological 

Economics 23(3): 251-264. 

Goldberg, D., 1989. Genetic Algorithms in search, optimization, and machine learning. 

Reading, MA: Addison-Wesley Longman Publishing. 

Grant, V., 1963. The origin of adaptations. Columbia University Press, New York. 

Gustafson, E. J., 1998. Quantifying Landscape Spatial Pattern: What Is the State of the 

Art? Ecosystems 1: 143-156. 

Hallogram Publishing, 2006. Evolver Software for Microsoft Excel. 

http://www.hallogram.com/evolver/index.html (last accessed October 15, 2006). 

Aurora, CO. 

Harris, G.A., 1967. Some Competitive Relationships between Agropyron spicatum and 

Bromus tectorum. Ecological Monographs 37: 89-111 

Hegazy, T., 2003. Resource Optimization using combined simulation and genetic 

algorithms. Journal of Construction Engineering and Management 129(6): 698-705. 

Hesseln, H., J.B. Loomis, D.B. Rideout, A. Gonzalez-Caban, 2004. Integrated Fuels Treatment 

Assessment: Ecological, Economic and Financial Impacts. Final Report. 99-1-1-05. 

Submitted to Joint Fire Science Program, Boise, Idaho. http://jfsp.nifc.gov. 

Higgins, S.I., and D.M. Richardson, 1996. A review of models of alien plant spread. Ecological 

Modelling 87: 249-265. 

Hull, A.C., 1965. Cheatgrass – a persistant homesteader. In Proeceedings from 

Symposium on Management of Cheatgrass on Rangelands, July 27-30, Vale, OR. 

Portland, OR: US Dept. of Interior, Bureau of Land Management: 20-26. 

Hunsaker, C.T. and D.A. Levine, 1995. Hierarchical approaches to the study of water 

quality in rivers. BioScience 45: 193–203. 

Interior Columbia Basin Ecosystem Management Project (ICBEMP), 2004. 

http://www.icbemp.gov/. Spatial online database. (Last accessed October 1, 2006) 

Interior Columbia Basin Ecosystem Management Project (ICBEMP), 2000. Interior 

Columbia Basin Final Environmental Impact Statement. Portland, Oregon: USDI 

Bureau of Land Management. December 2000. http://www.icbemp.gov/ 

Irwin, E. and J. Geoghegan, 2001. Theory, data, methods: developing spatially explicit 

economic models of land use change. Agriculture, Ecosystems and Environment

1764:1-18.
115 

Isard, W., C.L. Choguill, J. Kissin, R.H. Seyfarth, R. Tatlock, 1972. Ecologic-Economic 

Analysis for Regional Development. New York: The Free Press.

Jensen, P.A. and J. F. Bard, 2003. Operations Research Models and Methods. Hoboken, 

NJ: John Wiley and Sons, Inc. 

Jocedal, J. and S.J. Wright, 2006. Numerical optimization. New York: Springer 

Publishers. 

Johnson, M., L.J. Rew, B.D. Maxwell, and S. Sutherland, 2006. The Role of Wildfire in 

the Establishment and Range Expansion of Nonnative Plant Species into Natural 

Areas. Bozeman, MT: Montana State University Center for Invasive Plant 

Management. 

Jones, K.B., A.C. Neale, S.N. Maliha, R.D. Van Remortel, J.D. Wickham, K.H. Riitters 

and R.V. O'Neil, 2001. Predicting nutrient and sediment loadings to streams from 

landscape metrics: a multiple watershed study from the United States Mid-Atlantic 

Region. Landscape Ecology 16(4): 301-312. 

Keeley, J. E., 2004. Ecological impacts of wheat seeding after a Sierra Nevada wildfire. 

International Journal of Wildland Fire, 13, 73–78. 

Keeley, J. E., 2006. Fire management impacts on invasive plants in the western United 

States. Conservation Biology 20(2):375-384 

Keever, C., 1955. Heterotheca latifolia, a new and aggressive exotic dominant in 

Piedmont Old-Field succession. Ecology 36: 732-739. 

Kim, S. and D.R. Fesenmaier, 1990. Evaluating spatial structure effects in recreation 

travel. Leisure Science 12:367-381. 

Kinter, C.L. 2003. Comparative ecological genetics of Bromus tectorum (cheatgrass, 

downy brome) from native European, naturalized New Zealand invasive North 

American populations. PhD. Dissertation, Washington State University, Pullman, 

WA. 

Klemmendson, J.O. and J.G. Smith, 1964. Cheatgrass (Bromus tectorum L.). Botanical 

Review 30:226-61. 

Knapp, P.A., 1996. Cheatgrass (Bromus tectorum L.) dominance in the Great Basin 

Desert: history, persistence, and influences to human activities. Global 

Environmental Change 6(1): 37-52. 

Kotanen, P.M., J. Bergeson, and D.L. Hazlett, 1998. Habitats of native and exotic plants 

in Colorado shortgrass steppe: a comparative approach. Canadian Journal of 

Botany 74: 664-672. 

Landis, J.D., 1995. Imagining Land Use Futures: Applying the California Futures Model. 

Journal of the American Planning Association 61:438-457. 

Lawler, J.J. D. White, and L.L. Master, 2003. Integrating representation and 

vulnerability: Two approaches for prioritizing areas for conservation. Ecological 

Applications 13(6):1762–1772. 

Mack, R. N., 1991. The commercial seed trade: an early disperser of weeds. Economic 

Botany 45: 257-273. 
116 

Mack, R. N., 2000. Assessing the extent, status and dynamism in plant invasions: current 

and emerging approaches. in: The Impact of Global Change on Invasive Species (H. 

A. Mooney and R. J. Hobbs, eds.), Island Press, Covelo, CA, pp. 141-168. 

Mack, R. N. and D. A. Pyke, 1984. The demography of Bromus tectorum: The role of 

microclimate, predation and disease. Journal of Ecology 72: 731-748. 

Mack, R. N. and D. A. Pyke, 1983. The demography of Bromus tectorum L.: Variation 

in time and space. Journal of Ecology 71: 69-93. 

Mack, R. N. and J. N. Thompson, 1982. Evolution in steppe with few large hooved 

mammals. American Naturalist 119: 757-773. 

Mack, R.N., 2003. Plant naturalizations and invasions in the eastern United States: 1634-

1860. Annals of the Missouri Botanical Garden 90: 77- 90. 

Mack, R.N., 1981. The invasion of Bromus tectorum L. into western North America: an 

ecological chronicle. Agro-Ecosystems 7:145-165. 

Mack, R.N., 1986. Alien plant invasion into the Intermountain West: A case history. In: 

H. A. Mooney and J. Drake (Eds.), Ecology of Biological Invasions of North 

America and Hawaii, pp. 192-213. New York: Springer-Verlag. 

McConnell, K. and I. Strand, 1981. Measuring the cost of time in recreation demand 

analysis: An application to sport fishing. American Journal of Ag. Econ. 63:153-

156. 

McGarigal, K., S.A. Cushman, M.C. Neel, and E. Ene, 2002. FRAGSTATS: Spatial 

Pattern Analysis Program for Categorical Maps. Computer software program 

produced by the authors at the University of Massachusetts, Amherst. Version 3. 

Available at www.umass.edu/landeco/research/fragstats/fragstats.html 

Meinig, D. W., 1968. The Great Columbia Plain: a historical geography, 1805-1910. 

University of Washington Press, Seattle. 

Menakis, J.P., D. Osborne and M. Miller, 2003. Mapping the cheatgrass-caused departure 

from historical natural fire regimes in the Great Basin, USA. USDA Forest Service 

Proceedings. Gen. Tech. Rep. RMRS-P-29. Fort Collins, CO: U.S. Department of 

Agriculture, Forest Service, Rocky Mountain Research Station: 281-288. 

Miller, J. R. and M. J. Hay, 1981. Determinants of hunter participation: Duck hunting in 

the Mississippi flyway. American Journal of Agricultural Economics 63:677-684.- 

Mills, T. J. and F. W. Bratten, 1988. Economic efficiency and risk character of fire 

management programs, northern Rocky Mountains. Research Paper PSW-192. 

Berkley, CA: U.S. Forest Service, Pacific Southwest Forest and Range Experiment 

Station. 

Moody, M. E. and R. N. Mack, 1988. Controlling the spread of plant invasions: The 

importance of nascent foci. Journal of Applied Ecology 25: 1009-1021. 

Mosley, J.C., 1996. Prescribed Sheep Grazing to suppress cheatgrass: A review. Sheep 

and Goat Research Journal, 12(2):74-81. 
117 

National Survey on Recreation and the Environment (NSRE), 2000-2002. The 

Interagency National Survey Consortium, Coordinated by the USDA Forest Service, 

Recreation, Wilderness, and Demographics Trends Research Group, Athens, GA and 

the Human Dimensions Research Laboratory, University of Tennessee, Knoxville, 

TN. 

Naugle, D.E., K.E. Doherty, and B.L. Walker, 2006. Sage-grouse winter habitat selection 

and energy development in the Powder River Basin: completion report. Unpublished 

report, University of Montana, Missoula. 

Noon, C.E., F.B. Zhan and R.L. Graham, 2001. GIS-Based analysis of marginal price 

variation with an application in the identification of candidate ethanol conversion 

plan locations. Networks and Spatial Economics 2: 79-93. 

Novak, S. J., R. N. Mack and P. S. Soltis, 1993. Genetic variation in Bromus tectorum

(Poaceae): introduction dynamics in North America. Canadian Journal of Botany

71: 144-1448. 

Novak, S.J. and R. N. Mack, 2005. Genetic bottlenecks in alien plant species: influence 

of mating systems and introduction dynamics. Pp. 95-122. In: Exotic Species – Bane 

to Conservation and Boon to Understanding: Ecology, Evolution and Biogeography. 

(D. F. Sax, S. D. Gaines, and J. J. Stachowicz (eds.). Sinauer, MA. 

Novak, S.J. and R. N. Mack, 2001. Tracing plant introduction and spread into naturalized 

ranges: genetic evidence from Bromus tectorum (cheatgrass). BioScience 51: 114-

122. 

O’Neill, R.V., J.R. Krummel, R.H. Gardner, G. Sugihara, B. Jackson, D.L. DeAngelis, 

B.T. Milne, M.G. Turner, B. Zygmunt, S.W. Christensen, V.H. Dale, and R.L. 

Graham, 1988. Indices of landscape pattern. Landscape Ecology l(3): 153-162. 

O'Neill, R.V., C.T. Hunsaker, K.B. Jones, K.H. Riitters, J.D. Wickham, P.M. Schwartz, 

I.A. Goodman, B.L. Jackson, and W.S. Baillargeon, 1997. Monitoring environmental 

quality at the landscape scale. BioScience 47(8): 513-519. 

Optimization Online, 2006. Optimization Online links. http://www.optimizationonline.org/links.html (last accessed September 5, 2006). 

Palisades Corporation, 2006. RISKOptimizer: Simulation Optimization for Microsoft 

Excel Software. Version 1.0, October 2004. Computer software program produced 

by the Palisades Corporation, Newfield, NY. Available at: www.palisade.com. 

Pammel, L.H., J.B. Weems, and F. Lamson-Scribner, 1901. The Grasses of Iowa. Iowa 

Geological Survey Bul. No. 1. 

Papalambros, P.Y. and D.J. Wilde, 2000. Principles of optimal design: modeling and 

computation (2nd ed.) (http://www.optimaldesign.org/). Cambridge: Cambridge 

University Press. 

Parker D.C., S.M. Manson, M.A. Janssen, M. Hoffman, P. Deadman, 2003. Multi-agent 

systems for the simulation of land-use and land-cover change: a review. Ann Assoc 

Am Geogr 93(2):314–337

Pellant, Mike. BLM Coordinator Great Basin Restoration Initiative. Boise, Idaho. 
118 

Pellant, M., S. Jirik, J. J. Kaltenecker, 1999. Use of OUST® Herbicide to Control 

Cheatgrass in the Northern Great Basin. Proceedings of: Sagebrush Steppe 

Ecosystems Symposium, Boise State University, Boise, Idaho. June 21-23. 1999 

Peterson, E. B., 2003. Mapping Percent Cover of the Invasive Species Bromus tectorum 

(Cheatgrass) over a Large Portion of Nevada from Satellite Imagery. Report for the 

U.S. Fish and Wildlife Service, Nevada State Office, Reno, by the Nevada Natural 

Heritage Program, Carson City.

Phaneuf, D. J. and V. K. Smith, 2005. Recreation Demand Models, in Handbook of 

Environmental Economics. Volume 2. Valuing Environmental Changes, edited by 

K.G. Maler and J. Vincent, Amsterdam: North-Holland.

Pichitlamken, J. and B. L. Nelson, 2002. A combined procedure for optimization via 

simulation. Proceedings of 2002 Winter Simulation Conference. Institute of 

Electrical and Electronic Engineers, Piscataway, New Jersey. 

Pierson, E. A. and R. N. Mack, 1990. The population biology of Bromus tectorum in 

forests: distinguishing the opportunity for dispersal from environmental restriction. 

Oecologia 84: 519-525. 

Pyke, David A., 2005. Personal communications. USGS Forest and Rangeland 

Ecosystem Science Center, 3200 S.W. Jefferson Way, Corvallis, OR 97331 

Pyke, D.A., T.O. McArthur, K.S. Harrison and M. Pellant, 2003. Coordinated 

Intermountain restoration project: fire, decomposition and restoration. In N. 

Allsopp, A.R. Palmer, S.J. Milton, K.P. Kirkman, G.I.H. Kerley, C.R. Hurt and C.J. 

Brown (Eds.), Proceedings of the VIIth International Rangelands Congress, July 26-

August 1, 2003, Durban, South Africa. Durban, South Africa: International 

Rangelands Congress. 

Quigley, Thomas M.; Richard W Haynes, and Russell T. Graham. 1996. Integrated 

Scientific Assessment for Ecosystem Management in the Interior Columbia Basin 

And Portions of the Klamath and Great Basins . Gen. Tech. Rep. PNW-GTR-382. 

Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest 

Research Station. 310 p. 

Radeloff, V.C., R.B. Hammer, S.I. Stewart, J.S. Fried, S.S. Holcomb, and J.F. McKeefry, 

2005. The Wildland Urban Interface in the United States. Ecological Applications

15:799-805. http://silvis.forest.wisc.edu/projects/WUI_Main.asp. 

Rawlins, G., 1991. Formations of genetic algorithms. San Mateo, CA: Morgan 

Kaufmann. 

Rice, K. J. and R. N. Mack, 1991a. Ecological genetics of Bromus tectorum: I. A 

hierarchical analysis of phenotypic variation. Oecologia 88: 77-83. 

Rice, K. J. and R. N. Mack, 1991b. Ecological genetics of Bromus tectorum: II. 

Intraspecific variation in phenotypic plasticity. Oecologia 88: 84-90. 

Rice, K. J. and R. N. Mack, 1991c. Ecological genetics of Bromus tectorum: III. The 

demography of reciprocally sown populations. Oecologia 88: 91-101. 
119 

Riitters, K.H., R.V. O'Neill, C.T. Hunsaker, J.D. Wickham, D.H. Yankee, S.P. Timmins, 

K.B. Jones and B.L. Jackson, 1995. A factor analysis of landscape pattern and 

structure metrics. Landscape Ecology 10(1):23-29.

Roberts, Tom. Personal communications. National Science and Technology Center, 

Bureau of Land Management, Denver, Colorado. 

Roberts, T.C., 1990. Cheatgrass: Management implications in the ‘90’s, in U.S. Forest 

Service Intermountain Station. USDA Forest Service Proceedings, Symposium on 

Cheatgrass Invasion, Shrub Die-off, and Other Aspects of Shrub Biology and 

Management. Gen. Tech. Rep. INT-276. Provo, UT: US Department of Agriculture, 

Forest Service, Intermountain Station. 

Robichaud, Peter R. Jan L. Beyers, Daniel G. Neary, 2000. Evaluating the Effectiveness 

of Postfire Rehabilitation Treatments. United States Department of Agriculture, 

Forest Service, Rocky Mountain Research Station, General Technical Report 

RMRS-GTR-63. September 2000. 

Rofini, D. P., 1986. The role of Hoopes, Bro. & Thomas Nursery of West Chester, 

Pennsylvania in American horticulture. M.A. thesis, West Chester University, West 

Chester, PA. 

Rosenberger, R.S. and J.B. Loomis, 2001. Benefit transfer of outdoor recreation use 

values: a technical document supporting the Forest Service Strategic Plan (2000 

revision). Gen. Tech. Rep. RMRS-GTR-72. Fort Collins, CO: U.S. Department of 

Agriculture, Forest Service, Rocky Mountain Research Station: 59 p.

Ruiz, G.M. and J.T. Carlton (eds.), 2003. Invasive species: vectors and management 

strategies. Island Press, Washington, DC. 

Scott, J.M., C.R. Peterson, J.W. Karl, E. Strand, L.K. Svancara, and N.M. Wright, 2002. 

A Gap Analysis of Idaho: Final Report. Moscow, ID: Idaho Cooperative Fish and 

Wildlife Research Unit. 

Shaw, N.L. and S.B. Monsen, 1999. Controlling Annual Grasses with OUST® 

Herbicide. Restoration of Sagebrush Steppe Ecosystem Resource Values. 

Proceedings of: Sagebrush Steppe Ecosystems Symposium, Boise State University, 

Boise, Idaho. June 21-23. 1999 

Smith, A.E., 1995. Handbook of Weed Management Systems. New York: Marcel Dekker, 

Inc. 

Stewart, G. and A.C. Hull, 1949. Cheatgrass (Bromus tectorum L.) – an ecological 

intruder in southern Idaho. Ecology 30:58-74. 

Sutherland, R.J., 1982. A Regional Approach to Estimating Recreation Benefits of 

Improved Water Quality Journal of Environmental Economics and Management, 

September 1982, v. 9, iss. 3, pp. 229-47. 

Theobold, D. M., 2003. Targeting conservation action through assessment of protection 

and exurban threats. Conservation Biology 17(6):1624-1637. 

Theobald, D.M., 2005. Landscape patterns of exurban growth in the USA from 1980 to 

2020. Ecology and Society 10: 32. 
120 

Torrey, J., 1843. A flora of the state of New-York, comprising full descriptions of all the 

indigenous and naturalized plants hitherto discovered in the state; with remarks on 

their economical and medicinal properties. Carroll and Cook, Albany, NY. 

Troutman, J., 2006. Variational Calculus and Optimal Control: Optimization with 

Elementary Convexity (2nd ed). New York: Springer Publishers. 

Tutin, T.G., V.H. Heywood, N.A. Burges, D.H. Valentine, S.M. Walters, and D.A. Webb 

(eds.). 1964-1980. Flora Europaea. Cambridge, University Press, Cambridge, U.K. 

U.S. Army Corps of Engineers, 2002. Lower Snake River Juvenile Salmon Migration 

Feasibility Report/Environmental Impact Statement. Walla Walla District. 

U.S. Department of Interior (DOI) 1996. Effects of military training and fire in the Snake 

River Birds of Prey National Conservation Area. BLM/IDARNG Research Project 

Final Report. US Geological Surv., Biol. Res. Div., Snake River Field Station, 

Boise, ID. 130 pp. 

U.S. Fish and Wildlife Service, 2001. National Survey of Fishing, Hunting, and 

Wildlife-Associated Recreation. www.fws.gov 

U.S. Fish and Wildlife Service, 1995. Status Review Completed: Greater Sage-Grouse 

Not Warranted for Listing as Endangered or Threatened. News Release of January 7, 

1995. 

U.S. Fish and Wildlife Service, 2003. 2001 National and State Economic Impacts of 

Wildlife Watching. August, 2003. 

http://library.fws.gov/nat_survey2001_economics.pdf 

U.S. Forest Service (USFS), 2004. National Fire Occurrence Website 

http://www.fs.fed.us/fire/fuelman/fireloc.htm (Last accessed, October 12, 2006). 

Upadhyaya, M.K., R. Turkington, and D. McIlvride, 1986. The biology of Canadian 

weeds. 75. Bromus tectorum L. Canadian Journal of Plant Science 66: 689-709. 

Verburg, P.H., 2006. Simulating feedbacks in land use and land cover change models. 

Landscape Ecology 21:1171–1183. 

Villard, M.A., M.K. Trzcinski and G. Merriam, 1999. Fragmentation effects on forest 

birds: relative influence of woodland cover and configuration on landscape 

occupancy. Conservation Biology 13(4): 774–783. 

Volmer, Jennifer, 2005. Environmental Resource Specialist, BASF Corporation. 

Laramie, Wyoming. 

Wainger, L.A., D. M. King, J. Salzman, and J. Boyd, 2001. Wetland value indicators for 

scoring mitigation trades. Stanford Environmental Law Journal 20(2):413-478. 

Wainger, L.A. and D.M. King, 2002. Spatial Decision Support System for Applying 

Investment Criteria to Environmental Decision Making: The Case of NonIndigenous Invasive Plant Management. Final Report to USDA. Deborah Hayes, 

Project Manager. 

Weber, A., 1929. Theory of the Location of Industries (translated by Carl J. Friedrich 

from Weber's 1909 book). Chicago: The University of Chicago Press. 
121 

Whisenant, S.G., 1990. Changing fire frequencies on Idaho’s Snake River Plains: 

ecological and management implications. USDA Forest Service Proceedings, 

Symposium on Cheatgrass Invasion, Shrub Die-off and Other Aspects of Shrub 

Biology and Management. Gen. Tech Rep. INT-276. Provo, UT: US Department of 

Agriculture, Forest Service, Intermountain Station: 4-10. 

Whitehead, J.C. and T.C. Haab, 2000. Southeast Marine Recreational Fishery Statistical 

Survey: Distance and Catch Based Choice Sets. Marine Resource Economics

14:283-298. 

Wickham, J.D., R.V. O'Neill, K.H. Riitters, T.G. Wade and K. B. Jones, 1997. Sensitivity 

of selected landscape pattern metrics to land-cover misclassification and differences 

in land-cover composition. Photogrammetric Engineering and Remote 

Sensing 63(4): 397-402. 

Wisdom, Michael J. Personal communications. Research Wildlife Biologist.USDA 

Forest Service, Pacific Northwest Region, LaGrande Oregon. 

Wisdom, M. J., M. M. Rowland, L. H. Suring, L. Schueck, C. Wolff Meinke, B. C. 

Wales, and S. T. Knick, 2003. Procedures for regional assessment of habitats for 

species of conservation concern in the sagebrush ecosystem. March 2003 Report, 

Version 1, Pacific Northwest Research Station, 1401 Gekeler Lane, La Grande, OR 

97850. 

Young, J.A. and R.A. Evans, 1978. Population Dynamics after wildfires in sagebrush 

grasslands. Journal of Range Management 31(4):283-289. 

Young, J.A. and R.R. Blank, 1995. Cheatgrass and Wildfires in the Intermountain West. 

Proceedings of the California Exotic Pest Plant County Symposium. 

Zavaleta, E. 2000. The economic value of controlling an invasive shrub. Ambio. 

29(8):462-467. 

Zeleny, M., 1973. Multiple Criteria Decision Making. Columbia, SC: University of South 

Carolina Press.