UNR Economics Working Paper Series Working Paper No

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1 UNR Economics Working Paper Series Working Paper No The Economics of Fuel Management: Wildfire, Invasive Species, and the Evolution of Sagebrush Rangelands in the Western United States Michael H. Taylor, Kimberly Rollins, Mimako Kobayashi and Robin J. Tausch Department of Economics /0030 University of Nevada, Reno Reno, NV (775) Fax (775) December, 2011 Abstract In this article we develop a simulation model for estimating the economic efficiency of fuel treatments and apply it to two sagebrush ecosystems in the Great Basin of the western United States: Wyoming Sagebrush Steppe and Mountain Big Sagebrush. These two ecosystems face the two most prominent resource management concerns in sagebrush ecosystems relative to wildfire: annual grass invasion and native conifer expansion. Our framework simulates long-run wildfire suppression costs with and without fuel treatments explicitly incorporating ecological dynamics, stochastic wildfire, uncertainty fuel treatment success, and ecological thresholds. Our results indicate that fuel treatment is only economically efficient on the basis of wildfire suppression costs savings when the two ecosystems are in relatively good ecological health. Our approach also allows us to analyze how uncertainty about the location of thresholds between ecological states influences the economic efficiency of fuel treatments, as well as the influence of shorter wildfire return intervals and improved treatment success rates. JEL Classification: Q20, Q51, Q57 Keywords: Fuel Treatment; Wildfire; Sagebrush Ecosystem; Great Basin; Simulation Model; State-and-Transition Model; Ecological Thresholds

2 The Economics of Fuel Management: Wildfire, Invasive Species, and the Evolution of Sagebrush Rangelands in the Western United States Michael H. Taylor Kimberly Rollins Mimako Kobayashi Department of Economics, University of Nevada, Reno Robin J. Tausch USDA Forest Service, Rocky Mountain Research Station Reno, NV Abstract In this article we develop a simulation model for estimating the economic efficiency of fuel treatments and apply it to two sagebrush ecosystems in the Great Basin of the western United States: Wyoming Sagebrush Steppe and Mountain Big Sagebrush. These two ecosystems face the two most prominent resource management concerns in sagebrush ecosystems relative to wildfire: annual grass invasion and native conifer expansion. Our framework simulates long-run wildfire suppression costs with and without fuel treatments explicitly incorporating ecological dynamics, stochastic wildfire, uncertainty fuel treatment success, and ecological thresholds. Our results indicate that fuel treatment is only economically efficient on the basis of wildfire suppression costs savings when the two ecosystems are in relatively good ecological health. Our approach also allows us to analyze how uncertainty about the location of thresholds between ecological states influences the economic efficiency of fuel treatments, as well as the influence of shorter wildfire return intervals and improved treatment success rates. Keywords: Fuel Treatment, Wildfire, Sagebrush Ecosystem, Great Basin, Simulation Model, State-and- Transition Model, Ecological Thresholds Abbreviations: Wyoming Sagebrush Steppe (WSS), Mountain Big Sagebrush (MBS), State-and- Transition Model (STM), National Fire Danger Rating System (NFDRS) JEL Classifications: Q20, Q51, Q57 We acknowledge support from the Nevada Agricultural Experiment Station, the Joint Fire Science Program, through SageSTEP, and the USDA Agricultural Research Service "Area-wide Pest Management Program for Annual Grasses in the Great Basin Ecosystem" This is Contribution Number 69 of the Sagebrush Steppe Treatment Evaluation Project (SageSTEP), funded by the U.S. Joint Fire Science Program.

3 1. Background and Motivation Wildfire suppression costs in the United States have increased steadily over the last decades (Stephens and Ruth 2005, Calkin et al. 2005, Gebert et al 2007, Westerling et al. 2006, GAO 2007), with related expenditures by the U.S. Forest Service (USFS) and Bureau of Land Management (BLM) exceeding a billion dollars per year in four out of the seven years leading up to 2006 (Gebert et al 2008). This is in part due to a century of U.S. federal wildfire policy that focused on wildfire suppression without accounting for the resulting accumulation of fuel on the landscape (Reinhardt et al 2008; Stevens and Ruth 2005; Busenberg 2004; Pyne 1982; Egan 2009; Donovan and Brown 2007). Pre-fire fuel management treatments (henceforth, fuel treatments) have been recognized as an important tool for reducing wildfire damages and suppression costs for federal, state, and local agencies, as well as contributing to other landscape management goals (GAO 2007). 1 Public agency efforts and expenditures continue to emphasize wildfire suppression and post-fire rehabilitation over pre-fire fuel treatments. This may be explained, in part, by the lack of empirical work establishing the economic efficiency of fuel treatments (Hesseln 2000; Gebert et al. 2008). In this article we develop a simulation model for estimating the economic efficiency of fuel treatments and apply it to two sagebrush ecosystems in the Great Basin of the western United States. 2 Our framework simulates long-run wildfire suppression costs with and without fuel treatment, and takes into account the factors identified in Kline (2004) as necessary to evaluating the economic efficiency of fuel treatments. In particular, our approach accounts for (i) the cumulative cost of fuel treatments over time, (ii) the likelihood of wildfire events with and without treatments, (iii) the effects and costs of wildfire suppression and post-fire restoration, and (iv) the combined influence of management actions and wildfires on ecological conditions and ecological services over time. In accounting for all of these factors in a unified analysis, this article presents a framework that can be applied to evaluating the economic efficiency of fuel treatment in other ecosystem settings. To our knowledge, this article provides the first estimates of the economic efficiency of fuel treatments for sagebrush ecosystems. Previous work has evaluated the effectiveness of fuel treatments based on biophysical outcomes without attempting to monetize the benefits (Hartsough et al. 2009; Butry 2009), or has focused on other ecosystems (Loomis et al. 2002; Mercer et al. 2007). 3 Epanchin-Niell, Englin, and Nalle (2009) develop a simulation model to analyze the economics of post-fire rehabilitation for sagebrush ecosystems in the western United States. While similar in geographic scope and specification, the authors focus on post-fire rehabilitation treatments rather than pre-emptive fuel treatments. We analyze the economic efficiency of fuel treatments Wyoming Sagebrush Steppe (WSS) and Mountain Big Sagebrush (MBS) ecosystems. We focus on the WSS and MBS ecosystems because they face the two most prominent resource management concerns in sagebrush ecosystems relative to wildfire: The expansion of native conifers such as juniper and pinyon pine (Juniperus occidentalis, J. osteosperma; Pinus monophylla, P.edulis) in MBS systems, and the invasion of exotic annual grasses such as cheatgrass (Bromus tectorum) in both the WSS and MBS systems. The expansion of native conifers henceforth pinyon-juniper expansion has shifted fire regimes in MBS systems from relatively frequent and low to mixed severity wildfires (10 to 50 years mean fire return interval) to more infrequent and high severity wildfires (>50 years mean fire interval) (Miller and Rose 1999; Miller and Tausch 2001; Miller 1 Wildfire damages include damages to housing and other infrastructure, harm to human health from smoke and released particulate matter, post-fire soil erosion, and post-fire loss in agricultural production. 2 The Great Basin is an arid region in the western United States located between the Rocky and Sierra Nevada Mountains, and comprising most of Nevada and parts of Utah, California, Idaho, and Oregon. 3 Loomis et al. (2002) evaluate the effectiveness of prescribed burning to increase big game habitat in the San Bernardino National Forest in Southern California, where the benefits of big game habitat for hunters are measured using contingent valuation. Mercer et al. (2007) incorporate stochastic wildfire events and long-run economic consequences of fuel management in a Monte Carlo simulation to estimate the net economic benefits of alternative policies for Volusia County, Florida. 1

4 and Heyerdahl 2008). Similarly, annual grass invasion at the expense of native perennial species has reduced mean fire return intervals from >50 years to <10 years (Whisenant 1990). 4 In estimating the economic benefits of fuels treatment, our simulation model accounts for two main objectives of fuel treatments (Mercer et al 2007; Reinhardt et al 2009; GAO 2007). First, fuel treatments aim to reduce the probability of severe wildfires, and thus the expected costs of damages and suppression. Second, fuel treatments attempt restore health and resiliency to ecosystems, thereby limiting the spread of invasive species. 5 In addition, in an innovation relative to the previous literature (Epanchin-Niell, Englin, and Nalle 2009), our simulation model accounts for the complex relationship between invasive species and treatment success in WSS and MBS systems. Recent research has shown that the success or failure of fuel treatments in WSS and MBS systems is determined in large measure by whether or not a critical ecological threshold related to the presence of invasive species has been reached (McIver et al 2010). Our simulation model accounts for two key features of the relationship between fuel treatments, ecological change and wildfire. First, estimating the benefits of fuel treatment requires comparing how the landscape will evolve with and without treatment. We model rangeland ecosystem dynamics using the state-and-transition framework from rangeland ecology (Stringham, Krueger, and Shaver 2003). This framework describes a rangeland ecosystem as being in one of several ecological states, with states separate by ecological thresholds. The state-and-transition framework allows us to model both ecological succession within states and the role of wildfire as a catalyst of ecological change between states. In sagebrush ecosystems, depending ecological condition and the presence or absence of invasive species, wildfire can be a restorative force, helping to maintain ecosystem function in a desired ecological state, or a destructive force, moving rangeland into degraded ecological states (McIver et al. 2010). Second, it is necessary to take account how factors such as wildfire suppression costs, wildfire probabilities, and fuel management treatment costs vary with ecological condition. We use a variety of sources in this article to establish how these factors differ between ecological states in the WSS and MBS systems. Wildfire suppression costs for each ecological state in each system were obtained from data on 400 wildfires occurring from 1995 through 2007 in U.S. Forest Service Region 4. 6 Costs for the fuel management practices are obtained from the 2011 Natural Resource Conservation Service Utah Conservation Practice Cost Data. 7 Information on wildfire frequency and time to succession between ecological states is obtained from the LANDFIRE Rapid Assessment Vegetation Models. Section 3 provides a detailed discussion of the data and parameters used in the simulation. The benefits of fuel treatment are measured as the difference in the expected net present value of wildfire suppression cost with and without treatment. These benefits are then compared to treatment costs to evaluate economic efficiency. 8 A full accounting of the benefits of fuel treatments would require valuing all of the changes in ecosystem goods and services that are affected by treatments, such as reduced 4 Cumulative effects from pinyon-juniper expansion and annual grass invasion on sagebrush rangelands include increased wildfire activity, severity and suppression expenditures; diminished forage base for livestock, habitat loss for big game animals and sage brush obligate wildlife species, soil erosion and sedimentation, and decreases in air and water quality. 5 The U.S. General Accounting Office specifically notes these two objectives, stating that fuel reduction projects are intended to remove or modify wildland fuel to reduce the potential for severe wildland fires, lessen the damage caused by fires, limit the spread of flammable invasive species, and restore and maintain healthy ecosystems (GAO 2007). 6 U.S. Forest Service Region 4, the Intermountain Region, includes Wyoming, Utah, Idaho, Nevada, and portions of Colorado and California. 7 Fuel management practices considered in our simulation include herbicide treatments, reseeding, prescribed fire, and mechanical brush removal. 8 The trade-off between fuel treatment costs and expected reductions wildfire suppression expenditures is a central concern for the Bureau of Land Management and the U.S. Forest Service, agencies tasked with both aspects of wildfire management. In addition to the direct costs of wildfire suppression, increasing suppression expenditures strain agency budgets and resources, thereby diminishing capacity to meet other mandates, including fuel treatments. 2

5 wildfire damages, and improvements in wildlife habitat, forage livestock, recreation opportunities, and erosion control. Our model considers only wildfire suppression costs averted. Because we have not considered the additional benefits of fuel treatment, our results must be interpreted with caution. In particular, while our results allow us to conclude that fuel treatment is economically efficient in certain conditions; we are not able to conclude that treatment is not efficient in others. As is explained in Section 4, where there was uncertainty, parameters and model assumptions where chosen so as not to overstate the benefits or understate the costs of fuel treatment, thus our estimates understate the true economic benefits of fuel treatment. In this article we report all results on a per acre basis. This contrasts with the previous literature, which has focused on evaluating the benefits and costs of fuel treatment at larger spatial scales. 9 Reporting results in per acre terms has the advantage that it allows us to more readily consider how benefits and cost of fuel treatment differ depending on ecological condition, treatment costs, wildfire return interval, and other factors, and to analyze the question of optimal treatment timing given the dynamics of ecological succession. Assumptions and parameters are chosen in this model so that the per acre results can be scaled up to most spatial scales relevant for fuel treatment considerations; as such, relative to the previous literature, our analysis is more directly relevant to analyzing the economic efficiency of specific fuel treatment projects, which in practice are often small and targeted (100 acres, 500 acres, etc.; see Rideout and Omi 1995). We find that fuel treatments are economically efficient in the healthiest state in the WSS system, with expected net benefits of wildfire suppression costs averted of $ per acre. In contrast, we find that fuel treatments are not economically efficient in the two degraded ecological states in the WSS system (i.e., the decadent sagebrush and annual grass dominated states). In the MBS system, we find that the expected net benefits of treatment are small but positive in the healthiest rangeland state ($8.20 per acre), and are largest in the early stages of pinyon-juniper expansion ($ per acre). As in the WSS systems, we find that fuel treatments are not economically efficient in the two degraded ecological states in the MBS system (i.e., late state pinyon-juniper expansion and annual grass dominated). We find that fuel treatments are not economically efficient in degraded rangeland states despite large wildfire suppression costs savings because of the relatively high cost of treatment and the low probability of treatment success. Our model allows us to address the question of where to perform fuel treatments on an ecologically heterogeneous landscape given a fixed management budget. We address this question by calculating benefit-cost ratios of treatment in different ecological states. 10 We find that fuel treatments in the healthiest state in the WSS system have the highest benefit-cost ratio (13.3), which suggests that treating healthy land in the WSS system is the most efficient use of public resources for fuel management. Our analysis, however, does not consider how treatment costs, treatment success rates, wildfire return intervals, and wildfire suppression costs change over a heterogeneous landscape because of factors such as slope, aspect, wind behavior, spatial spill-over effects, etc. Integrating these factors into an analysis of how to target fuel treatments would require incorporating economic information into a fully spatial landscape scale ecological simulation model such as Shang et al. (2004). Including economic information into a more sophisticated landscape simulation model should be considered a long-run goal of the literature in economics on fuel treatments. Our simulation model allows us to address several addition questions relevant for wildfire management on rangeland ecosystems that have not been addressed in the previous literature. First, we analyze how 9 Loomis et al. (2002) evaluate benefits and costs of fuel treatments for the entire San Bernardino National Forest; Mercer et al. (2007) consider the entire county of Volusia, Florida; Epanchin-Niell, Englin, and Nalle (2009) analyze the benefits of restoration at the ecosystem scale. 10 As is explained in Section 5, net benefits from treatment on a landscape are maximized given a fixed budget by treating land with the highest benefit-cost ratios until the budget is exhausted. 3

6 uncertainty about whether or not an ecological threshold between states has been crossed influences the economic efficiency of fuel treatments. The transition between ecological states critically determines how rangeland ecosystems respond to fuel treatments, and it is often difficult for even experienced ecologists to determine whether a rangeland system has transitioned between states (McIver 2010). We find that uncertainty about whether an ecological threshold has been crossed substantially lowers the expected benefits from fuel treatment. Second, recent studies have suggested that current fire rotation intervals in sagebrush ecosystems are short relative to historic averages as a result of invasive species, changes in disturbance regimes, climate change, and other factors (Baker 2009b; Romme et al. 2009). We find that shorter fire return intervals increase the economic benefits from fuel treatment dramatically in all ecological states. Third, there is little information in the published literature on fuel treatment success rates. For this reason, we analyze the relationship between fuel treatment success rates and the expected net benefits from treatment. We find that in the WSS system, fuel treatments are only economically efficient in degraded ecological states if either treatment costs are decreased dramatically or success rates are increased dramatically. 2. Wildfire, Invasive Species, and Sagebrush Rangelands The sagebrush biome of the western United States occupies 100 million acres of western high desert, provides habitat for more than 300 species of wildlife, supports one of the fastest growing human populations in the nation, and is the primary forage base for the western livestock industry (Knick et al, 2003). 11 In this article, we focus on the two major invasive species issues in sagebrush ecosystems: pinyon-juniper expansion and annual grass invasion. Pinyon-juniper expansion and annual grass invasion have been identified as major contributors to the decline of sagebrush ecosystems in the Great Basin (Pellant 1994; Miller and Tausch 2001), and have caused sagebrush ecosystems to be considered among the most endangered in the North America (Noss et al. 1995; Bunting et al. 2002). Moreover, without effective management, the expansion of pinyon-juniper woodlands and invasive annual grasses is likely to continue in sagebrush ecosystem (Miller et al. 2000; Wisdom et al. 2002). Our analysis focuses on two sagebrush ecosystems that are under threat from these invasive species: the Wyoming Sagebrush Steppe (WSS) system, which is threatened by invasive annual grasses, and the Mountain Big Sagebrush (MBS) system, which is threatened by both native conifer expansion and invasive annual grasses. 12 WSS systems are generally found at elevations of roughly between 4,700 and 6,500 feet above sea level and comprise roughly 37.8 million acres in the Great Basin (26% of the 145 million acre Great Basin). MBS systems are generally found at elevations of over 6,500 feet and comprise 9.1 million acres in the Great Basin (6.3% of total area in the Great Basin). 13 The map in Figure 1 depicts the location of WSS and MBS systems in the Great Basin. Pinyon-juniper expansion and annual grass invasion have changed wildfire regimes in sagebrush ecosystems throughout the Great Basin. Through decades of over suppression of rangeland fires, expansion of pinyon pine and juniper trees from their historic ranges in upland areas into lower elevation sagebrush plant communities has led to an increase in the accumulation of woody fuels in these communities. This accumulation of woody fuels has led to less frequent, but more intense wildfire (Miller and Rose 1999; Miller and Tausch 2001; Miller and Heyerdahl 2008). On the other hand, annual grasses invasion has led to increased wildfire frequency and severity on invaded lands, and, because invasive 11 The majority of land in sagebrush ecosystems in the Great Basin is held in public ownership and managed by the Bureau of Land Management, the U.S. Forest Service and other public land management agencies. The Bureau for Land Management alone is responsible for over 60% of Great Basin lands (BLM, 1999, 2000). 12 Wyoming Sagebrush Steppe and Mountain Big Sagebrush systems are broad classifications that encompass many specific ecological site descriptions; however, available economic data (i.e. wildfire suppression costs and fuel treatment costs) are organized at to these broader classifications, thereby not permitting analysis at more specific degrees of ecological resolution. 13 Acreages calculated using Great Basin Restoration Initiative data (sagemap.wr.usgs.gov). 4

7 annuals are often the first species to reemerge post-fire, an escalating cycle of increasingly frequent wildfires in many areas (Whisenant, 1990; Miller and Tausch, 2001). If not adequately dealt with, the interaction between invasive species and wildfire is predicted to result in irreversible shifts in ecosystem dynamics, undermining the ability of sagebrush ecosystems to support native wildlife and plants, a sustainable livestock industry, and an array of watershed and recreation values (BLM, 2000; Pellant, Abbey, and Karl, 2004; Young et al, 1987; Devine, 1993). In addition to influencing wildfire frequency and severity, invasive species also influence how sagebrush ecosystems respond to wildfire. On relatively un-invaded rangeland, wildfire is an important contributor to ecosystem health by restoring native perennial grasses and resetting rangeland vegetation to early successional stages. 14 In contrast, in areas where annual grasses invasion has advanced beyond a critical threshold, wildfire results in increased prevalence of annual grasses (McIver et al 2010). Similarly, Pinyon-juniper expansion crowds out sagebrush plant systems and builds long-lived fuels: the more intense wildfires that result are often hot enough to alter soil chemistry and composition, impeding the ability of native plants to regenerate after wildfire, and leading to the establishment and eventual dominance of invasive annuals. In addition, rangeland ecologists have found that thresholds related to invasive species prevalence are important for determining how sagebrush ecosystems respond to fuel treatments. The relationship between invasive species, ecosystem response to wildfire, and fuel treatment success in WSS and MBS systems is described in more detail in the next section. 3. Ecological Dynamics: State-and-Transition Models We model rangeland ecosystem dynamics using the framework provided by state-and transition models (STMs) widely used in rangeland ecology (Stringham, Krueger, and Shaver 2003). The Natural Resource Conservation Service has adopted STMs as standards through which they collect and organize biophysical data for rangelands. 15 STMs describe ecosystems as being in one of several alternative ecological states that are separated by ecological thresholds. STM dynamics involve transitions between states, across these ecological thresholds. In sagebrush ecosystems, transitions between ecological states can be triggered by natural events such as drought, wildfire, and invasive plants, or by human activities such as livestock grazing, and can only be reversed with active (and often expensive) management effort (McIver et al. 2010; Briske et al. 2006). More degraded states are typically less likely to be reversed with management, while the healthier states are more resilient and resistant to transition. The stylized STMs for the WSS and MBS systems that are used in our simulation are described in this section. 3.1 Wyoming Sagebrush Steppe (WSS) Ecosystem We model WSS system as potentially existing in one of three ecological states. Figure 2a illustrates the stylized state-and-transition model that describes the ecological dynamics of the WSS system in our simulation model. Perennial grasses and sagebrush with a small presence of invasive annual grasses characterize the healthiest state, which will be referred to as WSS Wildfire and fuel treatment, 14 For example, in the absence of invasive annual grasses perennial grasses and herbaceous plants in WSS systems gradually give way to sagebrush and other shrubs. Aging healthy sagebrush plant communities generate increasing levels of dead woody material that fuel naturally igniting rangeland fires. Patches of bare ground between shrubs limit the spread and size of individual rangeland fires, which release nutrients and moisture to support re-emergence of perennial grasses. The sagebrush steppe evolved through this process as a mosaic of different-aged plant communities. Wildlife species especially adapted to this region, such as the threatened sage grouse, depend upon the close proximity of different stages in sagebrush/perennial grass succession. 15 The Natural Resource Conservation Service refers to STMs as the key component of an Ecological Site Description, as they depict and organize information regarding the ecological dynamics of an ecological site. The Ecological Site Description Database is a project to describe all relevant biophysical properties of landscapes nationwide, and the data is easily accessible ( 16 At this time and for the foreseeable future, consensus indicates that invasive annual grasses cannot be eradicated from the region accordingly, the healthiest states of each of our two models includes a small presence of invasive annual grasses with the implication that without management, these systems are likely to transition to cheatgrass-dominated states. 5

8 which acts as a surrogate for naturally occurring rangeland fire, maintains the system in WSS-1; however, without naturally occurring fire or fuel treatment, an ecological disturbance such as the overgrowth of sagebrush and other native shrubs, concomitant loss of perennials and increased presence of invasive annual grasses will cause the system to transition over time from WSS-1 to a new ecological state, WSS-2. WSS-2 is characterized by overgrown decadent sagebrush with reduced perennial grasses and increased annual grasses. Wildfire in WSS-2 is hotter and more intense, and suppression expenditures are greater, than in WSS-1. The transition from WSS-2 to WSS-1 is reversible only with rehabilitation effort, and the success of this effort is uncertain. Moreover, because of the loss of perennial plant vigor, wildfire in WSS-2 causes the system to transition to WSS-3. In WSS-3, invasive annual grasses are the dominant species, wildfires occur frequently, and the system can only be rehabilitated to WSS-1 with costly treatments with low success rates. Section 4 provides details regarding probabilities of treatment success, treatment methods and costs, and wildfire suppression costs in each state in the WSS system. 3.2 Mountain Big Sagebrush (MBS) Rangeland Ecosystem We model the WBS system as potentially occurring in one of four ecological states, as shown in Figure 2b. As with the WSS system, perennial grasses and sagebrush with minimal presence of invasive annual grasses characterize MBS-1. Naturally occurring rangeland fire and fuel treatments maintain the system in MBS-1; however, if the system remains MBS-1 for a long period without fire or fuel management, it will transition into the early stages of pinyon-juniper expansion, a state referred to as MBS-2. The transition to MBS-2 can be reversed only with rehabilitation effort, and fire in MBS-2 restores the system to MBS-1. Without fire or fuel treatment, the system will eventually transition from MBS-2 to a closed-canopy pinyon-juniper state, MBS-3 with minimal to no native perennial grasses and invasive annual grasses dominating in the understory. MBS-3 is characterized by less frequent but far more costly wildfires relative to MBS-2. A system in MBS-3 can be rehabilitated to MBS-1 only with costly management action with highly uncertain success. If wildfire occurs in MBS-3, the system immediately transitions to MBS-4, the annual grass dominated state. As in the WSS system, once invasive annual grasses dominate the system, wildfires are larger and occur more frequently. MBS-4 can only be rehabilitated to MBS-1 through costly treatments with very low success rates. The next section provides details regarding the probabilities of treatment success, treatment method and costs, and wildfire suppression costs in each state in the MBS system. 4. Data and Parameters This section describes the parameters and data used in our model. Tables 1 through 5 summarize all model parameters and data described in this section, including wildfire frequencies, suppression costs, treatment costs, and the transitions between ecological states in the WSS and MBS systems. 4.1 Fuel Management Treatments Treatment costs were obtained from the 2011 Natural Resource Conservation Service Utah Conservation Practice Cost Data. This database contains information on the typical cost of conservation practices in Utah in 2011, including per acre costs for the methods used in our simulation (e.g., herbicide treatments, reseeding, prescribed fire, mechanical brush removal) We assume that the costs of specific treatment methods are constant between states in the WSS and MBS systems, but that the appropriate suite of 17 The 2011 Natural Resource Conservation Service Utah Conservation Practice Cost Data figures reflect 2011 prices for the treatment options. The Natural Resource Conservation Service updates treatment costs if actual costs change by more than 10%. 18 The Natural Resource Conservation Service database is used in calculating cost shares for several programs including the Agricultural Management Assistance program, the Environmental Quality Incentives Program, and the Wildlife Habitat Incentives Program. 6

9 treatments varies by state. 19 Appropriate treatments include prescribed fire in the healthiest states, and mechanical removal of overgrown vegetation by mastication, chaining, and chain saws in degraded states. In all but the healthiest states, fuel treatments also include herbicide application and reseeding with desired species that can compete with invasive annual grasses. Tables 1a and 1b give fuel treatments and costs in each state in the WSS and MBS systems. The success of fuel management treatments is uncertain (McIver et al. 2010). For this reason, we model treatment outcomes (either success or failure) as uncertain. Because of the high degree of scientific uncertainty about treatment success rates and the complexity of the relationship between treatment success rates and factors such as precipitation, soil structure and timing of treatments, the success rates used in this simulation were chosen to be rough approximations under typical conditions in WSS and MBS systems. We evaluate the sensitivity of our results to our assumptions on treatment success rates in Section Wildfire Suppression Costs We obtained distributions of per-acre wildfire suppression costs for each STM state from data describing 400 wildfires occurring from 1995 through 2007 in U.S. Forest Service Region 4, the Intermountain Region, which includes Wyoming, Utah, Idaho, Nevada, and portions of Colorado and California. 20 The available data for wildfire suppression expenditures does not include a variable that directly identifies STM state at the site of each fire; however, it does include the National Fire Danger Rating System (NFDRS) fuel model category that is used by the US Forest Service, Bureau of Land Management and other agencies during a wildfire event to evaluate wildfire suppression strategy. 21 The correspondence between the ecological states in our stylized STMs for the WSS and MBS systems and the NFDRS fuel models is summarized in Table 2. For each wildfire, the data includes total suppression expenditure, equipment used, crew sizes, resources used, as well as factors that influence wildfire behavior and suppression strategy, including the value of and distances to threatened buildings and structures, weather conditions, and topography. In the simulation, a random draw from a distribution of per-acre wildfire suppression expenditures is taken each time a wildfire occurs in each state. We want the per-acre wildfire suppression cost distribution to reflect the fact that a given acre is more likely to burn in a large fire than in a small fire. To account to this in the simulation, we draw from a weighted distribution of per-acre wildfire costs from the data, with wildfire size used as weights. 22 Table 3 summarizes wildfire size and suppression costs for each state in the WSS and MBS systems. 19 The suites of treatments for each STM state modeled were selected with the help of Julie Suhr-Pierce from Natural Resource Conservation Service, Utah. 20 Wildfire suppression cost data, compiled according to the procedure described in Gebert, Calkin, and Yoder (2007), were made available to us by the U.S. Forest Service Rocky Mountain Research Station. The data include expenditure and fire characteristics reported in the U.S. Forest Services National Interagency Fire Management Integrated Database for wildfires whose suppression costs could be cross-identified with the Forest Service accounting system to verify accuracy of expenditure information. Gebert, Calkin, and Yoder (2007) explain that cross-identification is necessary because cost estimates in the NIRMID are largely inaccurate and should not be used for analysis. Cross-identification began with fiscal year Wildfires that grew together and were administratively treated as one wildfire complex were dropped from the data if it was not possible to accurately assign expenditures from individual fires to the fire complex (Gebert, Calkin, and Yoder 2007). 21 We match each state in the WSS and MBS models with NFDRS fuel model categories using Hal E. Anderson (1982) s Aids to Determining Fuel Models for Estimating Fire Behavior. MBS-1 (over 6,500 feet) and WSS-1 (between 4,700 and 6,500 feet) correspond to NFDRS fuel models T and L (perennial grasses with some shrubs). WSS-2 (mature shrub canopy) corresponds to NFDRS fuel model B. WSS-3 and MBS-4 (invasive annual grass dominated) correspond to NFDRS fuel model A. MBS-2 (PJ with mature shrubs) corresponds to NFDRS fuel model C. MBS-3 (Closed canopy PJ) corresponds to NFDRS fuel model F. See for NFDRS fuel model vegetation descriptions. 22 The weighting procedure was necessary because per acre wildfire costs in our data are much larger for smaller wildfires than for large wildfires. The correlation coefficient for wildfire size and per-acre suppression costs is for our sample of 400 wildfires. 7

10 The wildfire suppression cost data used in this paper is likely to understate actual wildfire suppression costs for two reasons. First, the data include only wildfires of over 100 acres (300 acres after 2003) that escaped initial suppression by local and state agencies. 23 Because smaller wildfires tend to have larger per acre suppression costs than larger wildfires, their exclusion implies that the distribution of per-acre wildfire suppression costs in our simulation may understate the actual distribution of per-acre wildfire suppression costs for all wildfires in the region. 24 The magnitude of any resulting overstatement, however, is likely to be small because the vast majority of burned acres are burned in large wildfires. For example, in data available through the Western Great Basin Coordinating Center on all wildfires in the western Great Basin between 2000 and 2007, escaped wildfires account for 99.7% of acres burned in WSS-1, 97.0% in WSS-2, and 98.9% in WSS-3. Second, because of the difficulty of obtaining wildfire suppression expenditure information from local and state agencies, these suppression costs are excluded from our analysis. The data include wildfire suppression expenditures incurred by the U.S. Forest Service between fiscal year 1995 to 2003, and suppression expenditures incurred by both the U.S. Forest Service and the U.S. Department of Interior, which houses the Bureau of Land Management, between fiscal years 2004 and Not including suppression expenditures from state and local agencies implies that the distribution of per acre wildfire suppression costs used in our simulation underestimates the true distribution of per acre suppression costs. However, between fiscal year 1995 and 2003, the USFS was the recorded protection agency, or lead protection agency, on 96% of wildfires in our dataset. Between fiscal years 2004 and 2007, either the U.S. Forest Service or the U.S. Department of Interior was the lead protection agency in 88% of wildfires in our dataset. That the U.S. Forest Service or the U.S. Department of Interior was the lead protection agency, and, hence, likely incurred the majority of wildfire suppression expenditures for the fires in our data set, implies that the magnitude of the understatement resulting from the omission of state and local suppression costs is likely to be small Wildfire Frequency We use wildfire return intervals specific to each ecological state in the WSS and MBS systems using LANDFIRE Rapid Assessment Vegetation Models accessed through the U.S. Forest Service s Fire 26, 27 Effects Information System. LANDFIRE models synthesize information for wildfire regime characteristics, vegetation composition, structure, and dynamics for 254 vegetation communities in the United States. The models are developed using available data, literature and expert opinion, and are peerreviewed by teams of scientists. Importantly for our application, the LANDFIRE models are the only source that provide wildfire regime characteristics including wildfire return intervals for specific ecological states from STMs. We use information from the Wyoming Sagebrush Steppe LANDFIRE model for our WSS system, and from the Mountain Big Sagebrush with Conifers LANDFIRE model 23 The data is for escaped wildfires, which, prior to fiscal year 2003, are wildfires greater than 100 acres, and starting in fiscal year 2003, are wildfires greater than 300 acres. Smaller wildfires are generally handled by local agencies. Suppression costs for these smaller fires are aggregated annually at a regional/local level, making it not feasible to obtain fire-specific suppression expenditures (Gebert, Calkin, and Yoder 2007). 24 The correlation coefficient for wildfire size and per-acre suppression costs is This inverse relationship between fire size and per acre suppression cost is likely to hold for wildfires smaller than the escaped threshold because the factors that drive up the per-acre cost for smaller fires, such as the fixed costs of equipment mobilization, are relevant for all fires. 25 Gebert, Calkin, and Yoder (2007) cite a U.S. Forest Service Rocky Mountain Research Station study that analyzes wildfire suppression expenditures for 216 fires where the U.S. Forest Service was identified as the lead agency but where suppression expenditures for all other federal, state, and local agencies is available. This study found that the U.S. Forest Service expended, on average, more than 90% of the money spent on these fires, and that the remaining 10% was split between the Department of the Interior and state/local agencies. 26 The U.S. Forest Service s Fire Effects Information System can be accessed at: 27 We calculate annual wildfire probabilities using wildfire return intervals from LANDFIRE Rapid Assessment Vegetation Models, rather than directly from the data we use to calculate wildfire suppression costs, because our wildfire data covers 13 years from , a relatively short span of time from which to infer annual fire probabilities (Baker 2009b, Romme et al 2009; Shinneman and Baker 2009; Floyd et al 2004; Wangler and Minnich 1996; Bauer 2006). 8

11 for our MBS system. The correspondence between the ecological states in our stylized STMs for the WSS and MBS systems and the plant communities in the LANDFIRE models is summarized in Table 2. We assume that the annual wildfire probability in each state is the reciprocal of the wildfire return intervals reported in the LANDFIRE models. 28 This is equivalent to assuming that wildfires occur according to a geometric distribution (i.e., the probability of a wildfire is constant and independent across years). 29 Table 4 reports annual wildfire probabilities used in the simulation for the WSS and MBS systems. The mean average fire return interval across points on a landscape and the fire rotation interval on a landscape are equivalent (Baker and Ehle 2001; Stephens, Martin, and Clinton 2007; Romme et al. 2009; Baker 2009b). 30,31 This equivalence means that the temporal aspects of wildfire for the single acre considered in our simulation model hold for an area of any size. This implies that our estimates of the benefits and costs of fuel treatment will hold for any size area that can be characterized by the WSS or MBS systems (i.e., for any size area where the ecological and fire behavior assumptions in this paper hold). We assume that in any one year either the entire area burns or none of the area burns. This assumption simplifies the analysis and does not change the generality of our wildfire assumptions concerning expected wildfire return intervals on the landscape. Recent studies have found that wildfire return intervals in both the WSS and MBS systems are different from historical patterns with a trend toward shorter intervals. For the WSS system, Baker (2009b) finds that recent fire rotation intervals are short relative to historic averages where Wyoming Sagebrush Steppe is common and cheatgrass invasion is extensive. For the MBS system with PJ expansion, Romme et note that the suite of current and upcoming broadscale (sic) environmental changes - warming temperatures, increasing tree densities in some areas, and expansion of fire-promoting species, such as cheatgrass - may all interact to dramatically increase the amount of burning in pinyon-juniper and other vegetation types over the next century. Because of these current and anticipated changes in wildfire frequency in both the WSS and MBS systems, in Section 5 we re-consider the benefits of fuel treatment for a range of wildfire frequencies believed to represent future wildfire activity in the WSS and MBS systems in the Great Basin Transitions with Wildfire In the simulation, we assume that fire in the healthiest state in either the WSS or MBS systems (i.e., WSS-1 or MBS-1) resets the system the earliest stage in each state, i.e., the stage with the maximum number of years until the system transitions to a degraded state without fire. We refer to this earliest stage as year 1. For example, if fire occurs in WSS-1, the system returns to year 1 in WSS-1 with 60 years 28 While the literature strongly suggests that disturbance including annual grass invasion shortens fire return intervals, there is little empirical basis to predict the magnitude of these changes. Because fire return intervals in the LANDFIRE models do not consider disturbances, our simulation using LANDFIRE parameters likely understates the current frequency of wildfire and, hence, the expected benefits of fuel treatments in our application. 29 By assuming that the probability of a wildfire is constant and independent across years, we ignore the role of fuel accumulation in the probability of a wildfire occurring. No research we are aware of describes how wildfire occurrence probabilities change with fuel accumulation. Our model uses average wildfire return intervals consistent with those in the LANDFIRE Rapid Assessment Vegetation Models. 30 The fire-return interval is the interval between two successive wildfires in a given area, where the size of the area is clearly defined. The U.S. Forest Service Fire Effects Information System Glossary distinguishes between the composite fire interval, which is the number of years between fires that scarred a certain portion of trees in an area (one tree, 10%, etc.), and point fire interval, which is the composite fire interval over a relatively small area considered to be a point. Alternatively, the fire rotation interval is the length of time required to burn the equivalent of a specified area. The definition of the fire rotation interval does not imply that the entire area will burn during a cycle; rather, some sites will burn several times and others not at all. The equivalency between average fire return interval across points on a landscape and the fire rotation interval on a landscape implies that the fire rotation interval can be estimated from the sample mean of point fire intervals, and, conversely, that the fire rotation interval provides the expected mean fire return interval for any point on a landscape. 31 Reed (2006) claims that the fire rotation interval is not equivalent to the average point fire return interval. Baker (2009b) demonstrates that Reed s claim is false and based on an error in his analysis. 9

12 until the system transitions WSS-2. If fire occurs in a state where annual grasses are heavily present in the understory, as is the case in WSS-2 or MBS-3, fire will cause the system to transition to the invasive annual grass dominated state. When the system is in the invasive annual grass dominated state, either WSS-3 or MBS-4, it will remain in this state after wildfire. Tables 5a and 5b summarize information on transition with wildfire for the WSS and MBS systems Transitions without Fire We assume that the WSS and MBS systems can only remain in the healthiest state for a finite amount of time in the absence of management treatment or fire before transitioning to a degraded state (i.e. WSS-2 or MBS-2). Times for ecological transition used in the simulation for the WSS system were taken from the Wyoming Sagebrush Steppe LANDFIRE model; time to transition for the MBS system was taken from the Mountain Big Sagebrush with Conifers LANDFIRE model. Times for ecological transition without wildfire are reported in Tables 5a and 5b Simulation Results In this section we report results on the benefits and costs of fuel treatments for two scenarios. First, Section 5.1 reports results for the WSS system under the assumptions (i) that one can observe with certainty which state the system is in, WSS-1 or WSS-2, and (ii) it is possible to observe how many years the system will remain in WSS-1 before transitioning to WSS-2. We refer to this scenario as the certain threshold scenario. Second, Section 5.2 reports results for the WSS system when these two assumptions are relaxed so that it is not possible to observe whether or not the threshold between WSS-1 and WSS-2 has been crossed, nor is it possible to observe the location of the system relative the threshold, i.e. the number of years until the transition would occur. These assumptions capture the fact that is often difficult for experienced rangeland ecologists to determine whether a system has transitioned between ecological states (McIver 2010). We refer to this second scenario as the uncertain threshold scenario. In Section 5.3 we analyze the relationship between treatment costs and treatment success rate for the WSS system; in Section 5.4 we analyze how the annual probability of wildfire influences our results for the WSS system; Section 5.5 reports results for the MBS in the certain threshold scenario. Our simulation model is stochastic. In each year, wildfire occurrences, treatment success given that treatment is undertaken, and per acre wildfire suppression costs are random variables. Each run of the simulation model considers the evolution of the landscape with and without fuel treatments over 200 years with different randomly generated realizations of wildfire and treatment success in each year. To generate our results, 10,000 runs of the simulation model are performed. To illustrate how the model works, Figure 3 reports results for 10,000 runs of the simulation model for fuel treatment performed in WSS-1. The results are reported on a per acre basis. Reporting results on a per acre basis allows our estimates of the benefits and costs of fuel treatments to be scaled up to larger spatial scale relevant for most treatment options. All results are presented in constant 2010 dollars; to calculate net present values (NPV), all dollar values are discounted at a constant rate of 3% The times to transition without fire reported in the LANDFIRE models do not take into account how disturbances such as annual grass invasion or pinyon-juniper expansion influence times to transition. Transitions between ecological states, however, necessarily imply some disturbance (Stringham, Krueger, and Shaver 2003). The directionality of the effect of disturbance on the time to transition is not controversial increased disturbance shortens the time to ecological transition however, the exact magnitude of these effects are not to our knowledge available in the peer-reviewed ecology literature. 33 A 3% discount rate is held to be the best estimate of the social time preference of consumers (Loomis 2002). The social rate of time preference (the rate that society is willing to trade off future consumption for current consumption) is considered the appropriate discount rate for decision-making by public agencies such as the National Oceanic and Atmospheric Administration (NOAA), the Department of the Interior (DOI), and the U.S. Environmental Protection Agency (US EPA) (Loomis 2002). 10

13 The results in this section focus on the net benefits of fuel treatment, which are the net present value (NPV) of the reduction in wildfire suppression cost resulting from treatment less the NPV of treatment costs. In addition, the model records the number of wildfires with and without treatment, the number of treatments performed, the number of successful treatments, and the final state of the system with and without treatment for each run of the simulation. Tables 6 and 7 report the mean value of these variables for the certain threshold case, as well as the 5 th percentile values and the 95 th percentile values. The mean values reported in Tables 6 and 7 can be interpreted as the expected values of fuel treatment taking into account the risk from stochastic wildfire and treatment success. A positive mean value of net benefits from fuel treatment indicates that the expected value of treatment is positive and that it is economically efficient for society to pursue treatment. Where to perform treatment on a heterogeneous landscape given a fixed budget can be analyzed by calculating expected benefit-cost ratios for different treatment strategies. Benefit-cost ratios are the appropriate metric for evaluating which types of land should be treated first because, given a fixed budget, net benefits are maximized by treating the land with the highest benefit-cost ratios until the budget is exhausted Wyoming Sagebrush Steppe: Certain Threshold Table 6 report the results from the simulation model for the certain threshold case and the initial state of the system is WSS-1, WSS-2, or WSS-3. The results reported in Table 6 assume the following treatment schedule. In WSS-1, treatment is applied in the final year before transition to WSS-2. As is describe in Table 5a, the WSS system can only remain in WSS-1 for 60 years in the absence of management treatment or wildfire before transitioning to WSS-2. It is always optimal to delay treatment in WSS-1 until just before the systems transitions to WSS-2 because this strategy delays the cost of treatment, and, as treatment is 100% successful in WSS-1, there is no risk associated with delaying treatment until just before the threshold. Moreover, delaying treatment increases the chances that the system will experience a wildfire, which are beneficial to rangeland health in WSS-1 and restore the system so that there is 60 years until the transition to WSS-2. In WSS-2 and WSS-3, the system is assumed not to change unless there is a wildfire or if fuel treatment is undertaken. This implies that if it is not economically efficient to treat in the current year in WSS-2 and WSS-3 then it is will never be efficient to treat. This also implies that if it is economically efficient to treat in WSS-3, then it will be economically efficient to perform treatment immediately following a failed treatment until a successful treatment occurs. 35 The results reported on Table 6 for the WSS-3 system are significant because they find that treatment in WSS-3 is not economically efficient (i.e., the expected net benefits are negative); however, the magnitude of the loss in net benefits from treatment in WSS-3 is inflated because the model predicts that treatment will take place in successive years until a successful treatment occurs even though treatment in WSS-3 is not efficient and should not be pursued. The results reported in Table 6 indicate that, given our assumptions and default parameters, the expected net benefits of treatment are positive only in WSS-1. In particular, expected net benefits from fuel treatment are $271.7 per acre in WSS-1, with a benefit-cost ratio of Treatment in WSS-1 is 34 Our analysis ignore two factors that can influence the decision of which lands to treat first on a heterogeneous landscape: (i) spatial interdependencies between adjacent parcels of land related to the effect of contiguous fuel on fire behavior and (ii) treatment costs generally decline with total area treated (Rideout & Omi 1995; Gonzalez-Caban 1997; Calkin and Gebert 2006; Mercer et al. 2007; Mercer and Prestemon 2008). Ignoring these two issues will not change our conclusions about which types of land should be treated first based on benefit-cost ratios unless either the spatial dependencies or returns to scale to treatment size differ systematically with rangeland ecological states. To our knowledge, no empirical work suggests that either factor differs systematically with rangeland states. Moreover, ignoring spatial dependencies or treatment returns to scale in will likely cause our model to understate the true net benefits because (i) spatial spillovers from treatment will lower the probability of wildfire on parcels that are adjacent to treated parcels, and hence increase treatment benefits, and (ii) lower per acre treatment costs as treatment size increases will lower treatment costs, and hence increase the treatment benefits. 35 The issue of treatments in consecutive years does not arise in WSS-2 because we assume that treatment in WSS-2 results in immediate transition to WSS-1 (success) or WSS-3 (failure). 11

14 economically efficient because it is relatively inexpensive ($19.50 per acre), 100% successful, and leads to a large reduction in the number of wildfires because it prevents transition of the system to WSS-2 and WSS-3. Fuel treatment is not economically efficient in WSS-2 because the appropriate treatment is expensive ($ per acre) relative to expected benefits from treatment ($132.8 in expected wildfire suppression cost savings). 36 An important reason why expected cost savings are low is that treatment in WSS-2 is successful only 50% of time, and the consequences of treatment failure is that the system transitions to WSS-3, which entails more frequent wildfires (treatment in WSS-2 leads to a reduction in the number of wildfires from 15.2 to 12.1 over 200 years). In WSS-3, repeated application of fuel treatment is effective at reducing wildfire suppression costs ($139.1 in expected wildfire suppression costs savings), but given the low probability of treatment success (2.5%), fuel treatment in WSS-3 is cost prohibitive. 37 Not surprisingly, the benefit-cost ratios reported in Table 6 indicate that the land in WSS-1 should be treated first (benefit-cost ratio of 13.3), and that treatment is not economically efficient in either WSS-2 or WSS-3 (benefit-cost ratios less than one). 38 Treated land in WSS-1 will always remain in WSS-1; without treatment, the model predicts that after 200 years the systems will have transitioned to WSS-2 7.3% of the time and to WSS % of the time. This indicates that treatment in WSS-1 is necessary to avoid the long-run conversion of the system to an annual grass dominated state (WSS-3). Treated land in WSS-2 will is evenly split between WSS-1 and WSS-3 because of the 50% treatment success rate; however, because treatment is found to be not economically efficient in WSS-2 given the model assumptions, the model predicts that treatment should not be pursued in WSS-2 despite the fact that it helps prevent the transition to WSS-3. Similarly, repeated treatment in WSS-3 over a 200 year horizon will lead to the rehabilitation of almost all the land to WSS-1 (98.9%), but the cost of repeated treatment (expected NPV of $2,526.9) does not justify the reduction in wildfire suppression costs (expected NPV of $139.1). Hence, despite the fact that repeat treatment in WSS-3 will lead to close to 100% restoration, it is still economically efficient for society to leave lands in WSS-3 from the perspective of reduced wildfire suppression expenditure. 5.2 Wyoming Sagebrush Steppe: Uncertain Threshold In this section we examine how uncertainty about the location of the system relative to the ecological threshold separating WSS-1 and WSS-2 influences the net benefits of fuel treatment, and analyze how this improved information changes the timing and efficiency of fuel treatments. We assume that the transition between WSS-1 and WSS-2 can occur with equal probability in each year within a range years. 39 In particular, we consider the cases where the threshold between WSS-1 and WSS-2 is located with equal probability between the 46 th and 75 th year, the 31 st and 90 th year, the 16 th and 105 th year, and the 1st and 120 th year after the system resets in WSS-1 (e.g., after a fire or a successful treatment in WSS- 1). 40 Figure 4 illustrates the expected net benefits from fuel treatment for these four cases when the appropriate treatment in WSS-1 is used (prescribed fire at $19.50 per acre). The appropriate treatment in 36 These results assume that a successful fuel treatment applied in either WSS-2 or WSS-3, whereby the system returns to WSS-1, is follow-up by treatment in WSS-1 in the year before transition to WSS-2. We would understate treatment benefits in WSS-2 or WSS-3 if we didn t allow successful treatment in either state to be followed up by the efficient treatment strategy in WSS These results indicate that treatment in WSS-1, which prevents transitions to WSS-2 and WSS-3, is economically efficient while treatment in WSS-2 or WSS-3, in an attempt to rehabilitate a degraded rangeland system, is not. However, because we do not include all of the ecological goods and services that are affected by changes in rangeland ecological state, we are not able to say anything conclusive concerning the efficiency of prevention relative to rehabilitation in Wyoming Sagebrush Systems. 38 A benefit-cost ratio of 13.3 for WSS-1 indicates that not only is fuel treatment efficient in WSS-1, but that the benefits are substantially greater than the costs even when the distortionary cost of raising public revenue is considered. Note that the distortionary cost of raising public funds will increase both the social cost of fuel treatments and the costs of wildfire suppression, which are also borne by public agencies, so that their effect on the magnitude of the benefit-cost ratios is ambiguous. 39 That is, we assume that the transition year is distributed according to a discrete uniform distribution within a range of years. 40 If, for example, the threshold is reached in the 31 st year, the system is in WSS-1 in year 30 and in WSS-2 in year

15 WSS-1 successful 100% of the time in WSS-1, but is never successful after the system has crossed the threshold to WSS The uncertain threshold case involves two costs relative to the certain threshold case: the cost of treating too late on some parcels and too early on others. Delaying treatment when the threshold is uncertain involves the risk of treating after the system has transition to WSS-2 on certain parcels (i.e., treating too late). The transition to WSS-2 lowers the probability of treatment success from 100% to 0% when WSS-1 treatment is used, and means that natural occurring wildfire will push the system to WSS-3. Treating earlier, however, involves the risk of bearing the costs of treatment earlier than necessary on some parcels (i.e., the costs treating too early). Treating too early also lowers the potential for a beneficial natural occurring wildfire in WSS-1. The results reported in Figure 4 demonstrate that for the where the threshold is located between the 46 th and 75 th year and the 31 st and 90 th year, the costs associated with delaying treatment (i.e., the risk of crossing the threshold to WSS-2 during the period of delay) are always greater than the benefits of delaying treatment (i.e., the benefits of delaying the cost of treatment and increasing the chance of a beneficial wildfire). For these two cases, net benefits are highest if treatment occurs in the final year before there is a risk of transition to WSS-1. Note that as in the certain threshold case reported in Section 4.1, it is always optimal to delay treatment when it is certain that the system is in WSS-1. For the case where the threshold is located between the 16 th and 105 th year and 1 st and 120 th year, early in the period of uncertainty, the benefits of delaying treatment are greater than the costs. 42 Net benefits from treatment are highest in year 20 for the case where the threshold is located between the 16 th and 105 th year and in year 25 in the 1 st and 120 th year case. In all four uncertain threshold cases considered in Figure 4 there is a point beyond which the net benefits become negative and it is no longer economically efficient to apply treatment. Because the probability of having crossed the threshold to WSS-2 increases each year, the probability of a treatment being successful declines each year, and there is a point beyond which treatment is not longer economically efficient. Figure 4 demonstrates that the expected net benefits from fuel treatment when there is less uncertainty about the ecological threshold separating WSS-1 and WSS-2. Net benefits are increase because the uncertainty about the location of the threshold means that treatments should take place earlier than they would if there was no uncertainty. Unsurprisingly, the net from treatment are highest when the threshold between WSS-1 and WSS-2 is crossed with certainty in the 61 st year ($271.70; see Section 4.1), and decline to $34.56 in the 46 th to 75 th year case, $32.90 in the 31 st to 90 th year case, $26.10 in the 16 th to 105 th year case, and $14.90 in the 1 st to 120 th year case. 5.3 Treatment Costs and Treatment Success Rate In this section, we analyze the relationship between fuel treatment success rate, treatment cost, and expected net benefits for the certain threshold case. Figures 5a and 5b illustrate the expected net benefits from treatment in WSS-2 and WSS-3 for a range of treatment success rates holding everything else constant. Recall from Section 4.1, we find that treatment is not economically efficient in either state under our default assumptions (i.e., a treatment success rate of 0.5 in WSS-2 and of in WSS-3). Not surprisingly, the net benefit from treatment is increasing monotonically in treatment success rate for 41 We do not report the results for the case when the appropriate treatment in WSS-2 is used (a combination of herbicide treatment, brush management, and reseeding at $ per acre) because we find that WSS-2 treatment is never economically efficient in the uncertain threshold case under the assumptions that it is successful 100% of the time in WSS-1 and 50% of the time in WSS-2. In addition, we do not report results for fuel treatment when the systems is in WSS-2 or WSS-3 with certainty for because, as with the certain threshold case reported in Section 5.1, we find that neither of treatment is economically efficient in the uncertain threshold case. 42 In part, this reflects the fact that when the period of uncertainty increases in length, the probability of the threshold being crossed each year, and, hence, the risk from delaying treatment, is smaller relative to when the period of uncertainty is shorter. 13

16 treatment in both WSS-2 and WSS-3. Given our default treatment cost of $205.35, treating in WSS-2 is economically efficient for success rates of 75% or higher; for WSS-3, treatment is economically efficient for success rates of 52% or higher at the default cost of $ These results indicate that treatment in either WSS-2 or WSS-3, which attempts to rehabilitate already degraded rangelands, are economically efficient in terms of wildfire suppression cost savings at sufficiently high treatment success rates despite the relatively high per acre costs (relative to treatment in WSS-1, which prevents the transition to degraded rangeland states). Figures 5a and 5b also illustrate the change in expected net benefits from a 1% change in treatment success rates. We label this the marginal product of a 1% change in treatment success rates. For treatment in WSS-2, the marginal product (the marginal change in expected benefits) is relatively stable at roughly $6.00. This indicates that regardless of the current treatment success rate, if a change in treatment success rate of 1% (resulting from a change in treatment method or intensity, or applying the results of scientific research aimed at increasing the effectiveness of fuel treatments) will pay for itself in terms of wildfire suppression cost avoided at a cost of roughly $6.00 per acre or less. For treatment in WSS-3, the marginal product ranges from roughly $100 when the treatment success rate is relatively low (in the region of 10%), and declines as the treatment success rate increases; however, for the range of treatment success rates where treatment is efficient in WSS-3 (52% or higher), the marginal product is stable at roughly $3.00. Figures 5c and 5d illustrate the break-even treatment cost for a range of treatment success rates. At the break-even treatment cost, the expected net benefits from treatment are not statistically different from zero. The region below the break-even curve (the shaded region in Figures 5c and 5d) contains all economically efficient treatment cost/treatment success rats combinations given our assumptions. Figures 5c and 5d confirm that our default treatment cost/treatment success rate combinations in WSS-2 and WSS-3 are not economically efficient, and that treatment in both states could become economically efficient if either the cost of treatment were lowered or the treatment success rate were increased Wildfire Frequency As discussed in Section 3, recent studies suggest that current fire rotation intervals on western rangelands are shorter relative to historic averages as a result of invasive plants, changes in disturbance regimes, climate change, and other factors (Baker 2009b; Romme et al. 2009). Because of these current and anticipated changes in wildfire frequency, in this section we reconsider the economic efficiency of fuel treatment for a range of wildfire frequencies for the certain threshold case. In particular, in Figures 6a and 6b we vary wildfire frequencies in WSS-2. We focus on changes in WSS-2 because this ecological state is compromised by invasive annual grasses and it is believed that it will experience large changes in wildfire frequencies relative to historic averages as a result. Figures 6a and 6b demonstrates that even a small reduction in the fire return in WSS-2, say from our baseline of 75 years to 50 years, will make fuel treatments in WSS-2 economically efficient. If, for example, the fire return interval in WSS-2 is shortened to 25 years or less because of annual grasses, then the net economic benefits from treatment in WSS-1 are $ compared to $ under our baseline fire return interval of 75 years; the net economic benefits from treatment in WSS-2 are $ compared to -$71.60 under our baseline assumptions. Rangeland ecologists suggest that fire intervals of 25 years or less are plausible for sagebrush rangelands where annual grasses dominate the understory. 43 It is reasonable to expect that that treatment costs and treatment success rates are positively related because higher treatment costs are driven by greater treatment intensity or a more effective treatment method. As such, there is also a positively sloped locus of the minimum costs to arrive at each treatment success probability. Information on this minimum cost loci used in combination with the information reported in Figures 5c and 5d on the break even treatment costs for WSS-2 and WSS-3 would make it possible to determine the economically efficient treatment cost/treatment success combination. To our knowledge, the data on the relationship between treatment costs and success rate necessary for the WSS system does not exist. 14

17 The results from the benefit-cost ratios in Figure 6b indicate that treatment is economically efficient in WSS-2 for wildfire return intervals in WSS-2 of 50 years or shorter. The benefit-cost ratios also indicate that for any wildfire return interval in WSS-2, the benefit-cost ratio is higher for WSS-1 treatment than for WSS-2 treatment. This indicates that for a given budget, land in WSS-1 should receive treatment first regardless of the wildfire return interval in WSS Mountain Big Sagebrush: Certain Threshold Table 7 reports the results from the simulation model in the MBS system for the certain threshold case. The results reported in Table 7 assume the following treatment schedule: as described in Table 5b, in the absence of treatment or fire, the system remains in MBS-1 for 129 years before transitioning to MBS-2, and remains in MBS-2 for 44 years before transitioning to MBS-3. As in the WSS system, it is always optimal to delay treatment in MBS-1 and MBS-2 until just before the system transitions to a new state because this strategy delays the cost of treatment, increases the likelihood of beneficial wildfire, and does not reduce the chances of treatment success. In MBS-3 and MBS-4, the system does not change unless there is a wildfire or if fuel treatment is undertaken. As in the WSS system, this implies that if it is not economically efficient to treat MBS-3 and MBS-4 in the current year, then it is will never be efficient to treat; and that if it is economically efficient to treat, then it will be economically efficient to perform treatment immediately following a failed treatment until a successful treatment occurs. 44 As is reported in Table 7, we find that, given our assumptions and default parameters, the expected net benefits from fuel treatment are $8.20 per acre in MBS-1 and $ per acre in MBS-2, and that fuel treatment is not economically efficient in either MBS-3 or MBS-4. These results mirror the results from the WSS system, where fuel treatments are economically efficient only in the healthiest ecological states. As in the WSS system, treatments are efficient in the healthiest states because treatment is 100% successful, relatively inexpensive, and prevents transition to MBS-3 and MBS-4, which entail frequent wildfires that are expensive to suppress. Fuel treatment is not efficient in MBS-3 and MBS-4 despite the large wildfire suppression cost saving associated with rehabilitation to MBS-1 because of low treatment success rates and relatively high treatment costs. The average benefit-cost ratio in MBS-1 is 5.2 and is 9.0 in MBS-2, which are both smaller than the average benefit-cost ratio in WSS-1 of This indicates that on a heterogeneous landscape, land in WSS-1 should be given priority for fuel treatment, followed by land in MBS-2 and land in MBS Conclusions In this article we develop a simulation for estimating the economic efficiency of fuel treatments and use it to provide the first estimates, to our knowledge, of the economic efficiency of fuel treatments in sagebrush ecosystems. We focus on the WSS and MBS systems, which are threatened by annual grass invasion and pinyon-juniper expansion. We find that in both systems, fuel treatments are economically efficient only on healthy land that has not transitioned to degraded states that require more costly rehabilitation with lower success rates. In addition, we find that uncertainty about the location of thresholds between ecological states lowers the economic efficiency of fuel treatments; that either treatment success rates have to be improved or treatment cost lowered, or some combination of the two, in order for fuel treatments to be economically efficient in degraded states in the WSS system; and that the shortening of historic wildfire return intervals in sagebrush systems predicted by rangeland ecologists are associated with a dramatic increase in the economic returns from fuel treatment. Results are reported on a per acre basis; assumptions and parameters are chosen so that these per acre results can be scaled up to larger spatial scales in ranges that are relevant for most range management decisions. 44 The issue of treatments in consecutive years does not arise in MBS-3 because we assume that treatment in MBS-3 results in immediate transition to MBS-1 (success) or MBS-4 (failure). 15

18 In addressing these question, we present an analytical framework that incorporates the factors identified by Kline (2004) as necessary for evaluating the economic efficiency of fuel treatments (these factors are discussed in the Introduction). In addition, our approach accounts for the two objectives of fuel treatment reducing wildfire risk and restoring ecosystem health and resiliency as well as the complex relationship between invasive species and treatment success. We capture ecological dynamics using the state-and-transition approach from rangeland ecology. In developing our model, we have created a framework that can be applied to evaluating the economic efficiency of fuel treatments in many ecosystems that can be described in the state-and-transition framework. This advance is important because the state-and-transition framework is increasingly being adopted by ecologists and as a data collection protocol and organizing analytical structure by U.S. government agencies such as the Natural Resource Conservation Service. Our results indicate when it is efficient from a societal perspective to invest in fuel management treatments. The results, however, cannot address the question of what portion of a public land management agency s budget it should direct towards fuels treatment. We cannot address this question in this article because the analysis implicitly assumes that that the funding for fuel treatments will not influence suppression activities in response to a wildfire. This assumption is not likely to hold for federal land management agencies contemplating large scale fuel treatments. If fuel treatment expenditures reduce budgets and resources for suppression, the likely outcome would be a reduction in per acre wildfire suppression expenditure when fuel treatment is pursued, but also higher damages to housing and other fixed structures, acres lost to agriculture, soil erosion, smoke and particulate matter released, etc., because of reduced suppression effort. Depending on the location of wildfires, the increase in wildfire damages may be greater than the reduction in wildfire suppression costs, which implies that the societal benefits of fuel treatment will be lower if treatment expenditure reduces the budget for suppression. 45 An interesting extension to this paper would be to analyze how the benefits and costs of fuel treatments differ between locations that are geographically close to population centers i.e., in the Wildland/Urban Interface (WUI) relative to more remote locations. We do not analyze this question in this article because of limitations in the available data. In particular, addressing how the benefits and costs of fuel treatments differ between WUI and non-wui areas requires information on how per acre wildfire suppression costs differ between areas. Our data on wildfire suppression costs, however, contains information on too few wildfires that occurred near population centers. 46 The lack of information on wildfires close to population centers can be attributed to the fact that the dataset contains only information on escaped wildfires, which are wildfires larger than a minimum size cut-off of 100 to 300 acres. It is likely that a higher portion of the wildfires whose ignition occurs near population centers are extinguished before they expand beyond this size because of the high costs of wildfire damages near population centers and the close proximity of wildfire fighting resources. 45 If wildfire fighting strategy reflects a least cost approach where the combined costs of suppression costs and wildfire damages are minimized, it follows that the increase in wildfire damages resulting from the decreases in suppression effort will be greater than the decrease in wildfire suppression costs. 46 For example, in the WSS system, no wildfires with ignition points within a mile of a population center are included in our data, and the closest ignition points to population center are 1.6 miles in WSS-1, 2.7 miles in WSS-2, and 1.5 miles in WSS-3. 16

19 Figures Figure 1: Great Basin Map 17

20 Figure 2a: Wyoming Sagebrush Steppe State-and-Transition Model Figure 2b: Mountain Big Sagebrush State-and-Transition Model 18

21 Figure 3: Fuel Treatment in WSS-1, Certain Threshold (10,000 runs) 19

22 Figure 4 20

23 Figures 5a-5d 21

24 22

25 Figures 6a and 6b 23