Study site and fuel treatment design

The study site was in Texas District 12 (TX12), one of the fire planning units of the Texas A&M Forest Service in East Texas, United States (Fig 1), covering 2,648,585 ha. In this district, on average, 480 wildfires occur annually, with a mean fire size of 8.9 ha; the largest recorded fire burned 404 ha in Smith County in August 2020 [40]. TX12 faces high wildfire risk based on reported indicators such as the wildfire threat index, value response index, and pine plantation response index [41]. Due to its proximity to dense human communities and diverse natural ecosystems, wildfires in this district are more likely to cause adverse socioeconomic and ecological consequences.

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Fig 1. Surface fuel distribution, representative fire locations (RFLs), and the experimental areas of the selected RFLs in the study site.

Dots indicate the centers of RFLs; numbers near the dots represent RFL numbers; red circles mark weather stations; small squares denote the RFLs selected for simulation experiments. Vegetation types or fuel models in the legend are described in S1 Table.

https://doi.org/10.1371/journal.pone.0342049.g001

The study site was recommended by Texas A&M Forest Service, a state agency responsible for vegetation fuel and wildfire management in Texas, so that the outcomes of this study can help guide fuel and fire management strategies and practices on the site and in similar forest ecosystems in the region. This is a modeling and simulation study that did not require physical access to the study site. Additionally, all data used in this manuscript, including the vegetation cover, forest inventory, past weather, terrain conditions, historical wildfires, and timber stumpage prices, are publicly available. Hence, no permits were required.

This site represents a forest-dominated ecosystem and an urban-wildland interface area that exists widely throughout the southern United States. Located in an ecological transition zone from Eastern Temperate Forests to Great Plains in the United States [42], it consists of diverse vegetation types and mixes ranging from forests to shrubs and to grasses (Fig 1, S1 Table, S2 Table) with a semi-arid climate [43–45]. The Eastern Temperate Forests component is represented by oak-hickory-pine mixed forests, with dominant tree species including various oaks (Quercus sp.), hickories (Carya sp.), and pines (Pinus sp.). The Great Plains component introduces natural grasslands, ranging from tall-grass prairie to, further south, mesquite-acacia savanna. Common fuel treatment objectives in this region include reducing wildfire risk to commercial pine plantations, protecting the expanding wildland-urban interface, and restoring fire-adapted ecosystems. Because the study area encompasses this range of conditions, findings about fuel treatment effectiveness here may provide insights into fuel and fire management in other regions.

For the tractability of simulations, we utilized the concept of a representative fire location (RFL), which represents a set of historical fire occurrences within an area of similar fuel characteristics and wildfire risk [41]. From a total of 46 RFLs, we randomly selected 10 RFLs to optimize the computational resources necessary for simulation while pursuing as much diversity in vegetation and land-use covers as TX12 can offer. Each RFL was assigned an experimental area of 10 km × 10 km, within which a set of simulations was performed. The relatively large experimental area allowed us to examine the effectiveness of fuel treatments at both site and landscape levels. While the RFLs in the west of the study site showed a high proportion of grassland and urban area, the RFLs located in the east were dominated by forestland (S2 Table).

We considered three fuel treatment options: non-treatment (NT), prescribed burning (PB), and thinning from below (TFB). PB and TFB are commonly used fuel treatment methods as well as silvicultural practices in the United States with TFB being more costly than PB [46]. PB, when properly implemented, can reduce surface and ground fuels without hurting bigger trees using controlled fires. TFB is a mechanical method to remove ladder fuels that help surface fires climb to tree crowns, creating more space between crowns to decrease the probability, spreading, and intensity of crown fires while lessening surface fire intensity. Although simulation studies have reported that mixed PB and mechanical treatments could be more effective than PB or thinning alone [47,48], we applied one treatment (NT, PB, or TFB) at a time (in each simulation) to an RFL. This approach enables keeping the experiments simple to clearly identify the effectiveness of each specific treatment relative to the baseline before investigating more complicated combinations.

Simulation and statistical analysis

Our overall modeling approach (Fig 2) consisted of three components: i) data preparation, ii) simulations of vegetation dynamics after fuel treatments and simulations of wildfire behaviors under different fuel treatment options and weather scenarios, and iii) regression analysis to assess the effectiveness of fuel treatments.

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Fig 2. Overall modeling approach including data processing, vegetation dynamics and wildfire simulations, and statistical analysis.

https://doi.org/10.1371/journal.pone.0342049.g002

Forest vegetation dynamics

We collected forest inventory data for the study site from the Forest Inventory and Analysis (FIA) database (FIADB) [49]. This database contained detailed information on the status and trends for all forests in the United States [50]. Specifically, the inventory information included the conditions and changes of the following: forest area and location; species, size, and health of trees; tree growth, mortality, and removals by harvest; wood production and utilization rates for various products; and forestland ownership [51]. The database was developed and updated periodically based on measurements from the permanent sampling plots established and distributed across forestlands in the United States, with 20% of the plots measured each year [51].

The inventory information was assigned to forest stands in each RFL. The assignment was based on the nearest sampling plot to the forest stand. The forest stands in the RFLs were identified using the fuel models from a map predefined and provided by the LANDFIRE program [52]. The map showed how surface fuel models were spatially distributed in a 30-meter grid spatial resolution. It consisted of the most common fire-carrying fuel types (grass, shrub, timber, or slash), fuel loading and surface area-to-volume ratios by size class and component, fuel bed depth, and fuel moisture of extinction [43]. We selected the pixels of forest-based fuel types and converted them into a forest stand distribution raster dataset. We assumed that one group of continuously connected pixels represented one forest stand and assigned a unique identification number to each pixel group. The distinct pixel groups were related to their nearest sampling plots from the FIADB.

After the forest stand was constructed, we used the Forest Vegetation Simulator (FVS) to simulate its dynamics including biomass growth and changes in stand structure and composition over time. Simulations using FVS require two inputs: a keyword record file and a tree data file. The former contains the user’s directions of the model, while the latter consists of tree-level information such as diameter and species [53]. The FIADB provides tree data files of the sampling plots in the form of FVS tables, and FVS uses those tables to simulate tree growth and yield in the plots.

FVS can also predict the effects of fuel treatments on the dynamics of a forest stand. We ran simulations without fuel treatment (NT) and with PB and TFB. The simulation outputs were collected at 1, 2, and 3 years after fuel treatment, respectively. In the simulations, PB was applied using mean weather conditions of early spring (February–March) before green-up, as recommended by the Texas Parks and Wildlife Department (S3 Table) [54], while TFB was implemented with a target residual basal area of 14 m²/ha, following guidelines from previous studies (S4 Table) [55,56]. Using the Fire and Fuels Extension to the Forest Vegetation Simulator (FVS-FFE) [57], the simulation outputs were converted into five predictors of potential fire activity: Fuel Model (FM), Canopy Cover (CC), Canopy Height (CH), Crown Base Height (CBH), and Crown Bulk Density (CBD). These predictors were combined with topographic predictors (elevation, slope, and aspect) to produce an input file for the fire behavior simulator in the landscape format (.lcp) at a 30-meter spatial grid using ArcFuels 10 [58].

Wildfire behavior

We used the FlamMap fire mapping and analysis system to simulate fire behavior. The system can analyze and depict potential fire behavior such as rate of spread, fire intensity, and crown fire using fuel and environmental conditions as input [59]. FlamMap consists of several fire behavior models including FARSITE. We selected FARSITE as a primary modeling system because it can utilize sequentially changing weather conditions, which were not available in other models.

FARSITE requires a landscape file, a weather condition file, an initial fuel file, and an ignition location file as input. The landscape file describes characteristics of the simulation landscape including slope, aspect, elevation, fuel model, canopy cover, canopy height, crown base height, and crown bulk density. This file was produced in the previous step using outputs from FVS-FFE combined with topographic variables and formatted into the required landscape format. The weather condition file includes the hourly data of temperature, relative humidity, precipitation, wind speed, wind direction, and cloud cover. The initial fuel moisture file is composed of the percentages of fuel moisture according to fuel characteristics: 1-hour dead fuel, 10-hour dead fuel, 100-hour dead fuel, herbaceous live fuel, and woody live fuel. The ignition location file shows where a fire starts.

With these inputs, FARSITE produces a set of simulated fire behaviors including arrival time, flame length, rate of spread, and perimeters at the same spatial resolution of the input landscape file. In this study, simulations were conducted at a 30-meter grid resolution, with additional settings—such as spot fires, crown fires, and perimeter/distance resolution—detailed in S5 Table. It also generates the fire growth report that summarizes burned areas for a specific simulation time.

The weather data were downloaded from Mesowest [60]. This dataset included hourly records of relative humidity, air temperature, and wind speed from different weather stations. Four weather stations were considered, which were the nearest stations to the selected RFLs, including Gilmer, Linden, Henderson, and Clarksville (Fig 1). We created 30 weather scenarios based on the Hot-Dry-Windy index (HDW) calculated from the dataset [61]. HDW is defined as:

where U, T, and RH are wind speed (m/s), air temperature (°C), and relative humidity (%), respectively.

Wind speed was measured at 6.1 m above ground, while temperature and relative humidity were measured at 2.0 m [62]. That is, HDW is composed of two effects of weather condition: the effect of wind and the effect of atmospheric heat and moisture. Wind affects both the rate of fire spread and the drying of fuels, with a higher wind speed accelerating fire propagation and promoting faster fuel drying. Atmospheric heat and moisture influence fire behaviors by modifying the evaporation rate of fuel moisture. Intuitively, HDW combines them into one indicator with a higher HDW value indicating conditions prone to more active fires. We focused on weather scenarios of high HDW values because mega fires have often been associated with severe or anomalous weather conditions [63–66], and the main objective of fuel treatments is to alleviate mega fires and their catastrophic impacts [67–69]. Conducting analyses on a diverse array of meteorological conditions is helpful for understanding the bigger picture. However, evaluating the effectiveness of fuel treatments under these most destructive scenarios is more urgently needed to ensure our preparedness for mitigating large, high-intensity wildfires that pose the most significant threat to ecosystems and communities. The high HDW values represented the 95th percentile of its hourly observations during the two simulation experiment years (21 April 2019–20 April 2021). Each weather scenario represented continuous weather records for 24 hours with the starting weather condition reflecting a high HDW value randomly selected from the 95th percentile and a starting time randomly selected between 6 and 17 hours of the day. In other words, after a starting HDW value and a starting time were selected, the historical weather records for the next 24 hours constituted a weather scenario.

We applied fuel treatments (NT, PB, and TFB) to each RFL where a circular treatment area with a 1.35 km radius was located at its center. The circular treatment area was chosen over other shapes partly because it is more likely to cover variations in terrain (e.g., aspect and slope), weather (e.g., wind speed and direction), and vegetation/fuel conditions (related to terrain and weather at least) at a given location and partly because it simplifies the selection of fire ignition points inside and outside the treatment area (described below). The radius of the circular area was set to be 1.35 km given the considerations of fire response time (from fire ignition/detection to initial response), fuel treatment cost, and average size of forest tracts owned by landowners, particularly private landowners (major landowner group) in the study region.

To assess both site- and landscape-level effects, we simulated fires igniting at random distances from the treatment boundary in each RFL. Specifically, ignition points were randomly selected within a range of [-d, + d] relative to the boundary. We assumed that a fire can start equally likely from any location point of [-d, + d]. Based on our simulation outcomes of fires starting from the center of the treatment area, we selected d = 0.65 km that would allow for approximately 50% of fires to burn across the treatment boundary. We randomly selected fire ignition locations from each quadrant of a RFL to represent the variations in terrain, weather, and vegetation conditions. In cases where a randomly selected ignition location did not develop into a fire (e.g., in a non-burnable area), we relocated that ignition point to the nearest burnable location. The shape and size of the fuel treatment area and the fire ignition locations were so designed that fire simulations would generate statistically adequate and valid data for evaluating and comparing both site- and landscape-level effectiveness of fuel treatments.

We conducted a total of 10,800 wildfire simulations across 10 RFLs. For each RFL, we modeled three fuel treatment scenarios (NT, PB, and TFB) combined with three post-treatment fire occurrence timings (τ = 1, 2, and 3 years), four randomly selected ignition locations inside and outside the treatment area, and 30 distinct weather scenarios. This resulted in 1,080 simulations per RFL. Following the simulations, we extracted spatial fire behavior outputs across all grid cells, including fire arrival time, flame length, fire intensity, and rate of spread. From the fire arrival time data, we calculated hourly cumulative area burned for each of the 24 simulation hours. We selected Area Burned (AB) as the primary response variable to represent the overall extent of wildfire. This metric is widely used for assessing landscape-level fire impacts, which allows our results to be readily comparable with the existing body of literature [28–31]. To provide a broader understanding of treatment effectiveness, we supplemented this primary analysis by modeling four other fire behavior metrics that drive fire severity and ecological effects: flame length (FL), fireline intensity (FI), crown fire activity (CFA), and rate of spread (ROS).

Fire behavior model validation

We validated FARSITE parameters using two historical fires near our study site: the Mayfield Fire and the Clear Lake Fire. The Mayfield Fire took place in a grassland-dominated landscape while the Clear Lake Fire occurred in a forestland-dominated area. Both forest and grass/shrub vegetation covers were chosen for validation because the RFLs selected for this study contained a mix of forest and grass/shrub vegetation types (Fig 1, S2 Table). There were no fuel treatments on these validation sites. More details about these two fires are described in S6 Table.

The observed perimeters were obtained from the Wildland Fire Interagency Geospatial Services Current Interagency Fire Perimeters dataset [70]. The characteristics of the simulation landscape were derived from LANDFIRE [52]. The weather data were downloaded from the nearest Remote Automatic Weather Station (RAWS) on the RAWS USA Climate Archive site [71].

We used the widely-adopted Sorensen metric (SM) [72] to compare the observed and simulated fire perimeters and area burned (S1 Fig.) [73–77]. The metric is defined as:

where A is the area burned included in both the observed and simulated perimeters (correct estimate), B is the area burned included only in the observed perimeters (underestimate), and C is the area burned included only in the simulated perimeters (overestimate). Observed and simulated fire perimeters and area burned are considered to be in substantial agreement if the SM value is between 0.6 and 0.8 [72,75]. The calculated SM value for the Mayfield Fire and the Clear Lake Fire was 0.77 and 0.68, respectively (S7 Table).

Economic impact estimation

Besides area burned, we were also interested in the sum of fuel treatment costs and economic damage caused by wildfires, referred as total cost herein. We focused on the damage of timber loss to wildfire, which reflected a major concern for private landowners in the study area where most forestlands were privately owned [78]. The post-TFB basal area closely aligns with silvicultural recommendations, which support long-term timber productivity and quality [79–81]. Similarly, properly designed and applied PB can reduce surface fuel loads without undermining timber productivity. While it may cause some mortality of smaller trees, which is often intended in silviculture for stand density control in overstocked forests where fire risk is also high, PB can improve forest health and stimulate tree growth. We designed and applied the PB treatment in the simulations based on silvicultural guidelines and practices in the region, thus causing little negative impact on long-term timber yield [82].

We estimated timber loss by integrating spatially explicit fire behavior from FARSITE with stand-level vegetation data from FVS at a 30-meter grid resolution. For each burned grid cell, total timber loss was calculated by multiplying the standing timber volume by the probability of tree mortality:

where i represents an individual grid cell, N denotes the total number of burned cells, Vol_i represents the standing timber volume for grid cell i, and Pm_i shows the probability of tree mortality for grid cell i. While the concept of tree mortality is embedded within the FVS-FFE post-fire logic, we employed these mortality functions explicitly at the pixel level to capture the spatial heterogeneity of fire behavior across the landscape. Pm was determined using a logistic function based on bark thickness (b) and the percentage of crown volume scorched (c) [83]:

Bark thickness is defined as , where v is a bark thickness parameter and d is the tree diameter. The percentage of crown volume scorched is calculated as , where s is the scorch height and l is the total crown length. We derived the scorch height (s) for each pixel based on the fireline intensity values simulated by FARSITE. Tree-level attributes—including species, diameter (d), and crown length (l)—along with the standing timber volume (Vol) were provided by FVS based on the nearest forest inventory plot data to that cell. By calculating mortality independently for every pixel, this approach explicitly accounts for the spatial heterogeneity of fire behavior and tree characteristics across the burned landscape. Finally, the total timber loss for a simulated wildfire was determined by summing the estimated losses from all affected grid cells within the landscape.

The damaged timber value was calculated by multiplying the 5-year average stumpage price (US$/m³) [84] by the damaged timber volume for each tree species. This calculation assumed a 100% loss of pre-fire stumpage value for mortality-affected timber. It might overestimate the economic damage because it did not account for potential salvage logging revenue. However, salvaged timber is often used only for producing low-value products. Given the rising logging cost and the low price of low-quality timber in the study region, including the value of salvaged timber is unlikely to considerably change the estimated timber loss value. Finally, we aggregated the timber losses across all grid cells within a landscape area to yield the total timber loss value at the landscape level. We calculated fuel treatment costs, based on the regional costs and trends for southern forestry practices [85]. We used a cost of US$77/ha for PB and US$356/ha for TFB, respectively.

Statistical analysis

We analyzed the effectiveness of fuel treatments using the Gaussian Generalized Linear Model (GLM) approach to estimate the relationship between a response variable and a set of explanatory variables, which were selected based on previous studies on wildfire behavior [86–88] and fuel treatment effectiveness [89–92]. We considered two response variables, area burned (AB) and total cost of fuel treatment and timber loss (TC) (Table 1). We used the bidirectional stepwise variable selection method to determine the best set of explanatory variables. We also considered interaction terms of explanatory variables based on the interaction hierarchy, effect sparsity, and effect heredity principles [93] and the literature on fuel treatment effectiveness [32,94–96].

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Table 1. Descriptions of variables included in the regression models.

https://doi.org/10.1371/journal.pone.0342049.t001

Starting from the base model consisting of one constant (one constant and all possible explanatory variables and their interaction terms), this method attempted to add or delete one variable in each step so that the statistical quality of the model improved. If adding or removing an additional variable did not improve the model’s quality, then the process stopped and the best model was identified. The metrics used to guide the selection of explanatory variables included the Akaike Information Criterion (AIC) for measuring the overall goodness of fit and the variance inflation factor (VIF) for detecting multicollinearity [97,98]. While stepwise selection methods have limitations, such as overfitting or multicollinearity [99,100], we employed this approach as a systematic tool to reduce a large set of potential predictors to a parsimonious and interpretable final model. The statistical analysis was conducted using R [101].

We then obtained the following regression model for both response variables:

where i represents RFLs, τ shows the number of years since fuel treatment when the fire occurs, h denotes the number of hours since the fire is ignited, j indicates the regression coefficients (β’s) for X, ε is the error term, and all variables are explained in Table 1 with X representing T, WS, and RH. The inclusion of the weather variables, T, WS, and RH, in the model was to remove their effects on the FARSITE-simulated outputs because they were also the input variables of FARSITE. As such, the estimated regression coefficients associated with the weather variables were not be interpreted. We selected the semi-log (response) function after testing and comparing it with linear, log-log, and semi-log (explanatory) forms. We also tested for potential spatial autocorrelation, homoscedasticity, and multi-collinearity in our models. The models were fit using our FARSITE simulation output and economic impact estimation data (S1 File). Table 1 summarizes the descriptive statistics of the response and explanatory variables.

To provide a clear framework for evaluating treatment performance, we distinguished between site-level and landscape-level effectiveness based on the ignition location and boundary-crossing behavior of a fire. Site-level effectiveness refers to scenarios where a fire starts and remains entirely within the boundaries of a treated area (d < 0 and Bdtn = 0). In contrast, landscape-level effectiveness represents the treatment impact where fires burn across treatment boundaries—where a fire either ignites within and spreads beyond a treated area (d < 0 and Bdtn = 1) or ignites in an untreated area and spreads into a treated area (d > 0 and Bdnt = 1).

To explore the treatment effectiveness beyond area burned and total cost, we also considered four other fire behavior metrics, including flame length (FL), fireline intensity (FI), crown fire activity (CFA), and rate of spread (ROS). We fit a regression model for each of these metrics using the same set of explanatory variables and interaction terms shown above (S8 Table), respectively. Using the same set of independent variables made it convenient to compare the treatment effectiveness between different fire behavior metrics. The statistical results for these supplementary models are provided in the Supporting Information (S9–S12 Tables).

Wildfire simulation results

There are considerable variations in the area burned and total cost, which indicates a wide-ranging dataset for regression analysis. Such variations were illustrated in S2 Fig, which shows different responses of fire perimeters to fuel treatment options in two different years after treatment in three RFLs. For instance, in RFLs 20 and 33, the fires starting inside the treatment area tended to have a smaller area burned than those starting outside the treatment area, but the opposite was true for RFL 43. From 2019 to 2021 (a delay of two more years in fire occurrence after treatment), the fires starting inside the treatment area in RFL 20 burned larger areas, but this delay effect was less obvious for the fires starting outside the treatment area in RFL 20, inside the treatment area in RFL 33, or inside and outside the treatment area in RFL 43.

The descriptive statistics of area burned (AB) and total cost (TC) provide further evidence of these variations (S3 and S4 Figs). The means of AB did not differ significantly across non-treatment (NT), prescribed burning (PB), and thinning from below (TFB) if all RFLs were considered. In contrast, of the three treatments (NT, PB, and TFB), TFB had the lowest mean of AB in the high-biomass RFLs (RFLs 20, 30, and 39; mean Bm = 155.2 m³/ha), whereas PB had the lowest in the low-biomass RFLs (RFLs 16, 41, and 44; mean Bm = 28.8 m³/ha). The mean of TC for PB and TFB was similar but lower than that of NT in the high-biomass RFLs, but PB had the lowest mean of TC in all RFLs and the low-biomass RFLs.

Regression results

Two semi-log regression models were estimated. One showed the statistical relationship between hourly accumulative area burned (AB) and a set of explanatory variables including fire duration (h), fuel treatment options (PB and TFB), fire spreading from the treatment area to the non-treatment area (Bdtn) or from the non-treatment area to the treatment area (Bdnt), timber volume (Bm), delay in fire occurrence after treatment (τ), distance of the ignition location from the treatment boundary (d), and their interaction terms (Table 2). The Moran’s I test did not detect spatial autocorrelation for both AB (p = 0.215) and TC (p = 0.471) models. The values of the variance inflation factor (VIF) did not show evidence of multicollinearity either (Tables 1 and 2). To avoid the heteroscedasticity problem, we utilized the Gaussian Generalized Linear Model (GLM) approach.

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Table 2. The estimated regression model for area burned.

https://doi.org/10.1371/journal.pone.0342049.t002

The other model depicted the relationship between total cost of fuel treatment and timber loss (TC) and the explanatory variables (Table 3). For the purpose of interpreting our modeling results, we defined ‘site-level’ effectiveness as scenarios where fires ignited and remained within the treated area (i.e., d < 0 and Bdtn = 0). In contrast, we defined ‘landscape-level’ effectiveness as scenarios where fire crossed the treatment boundary, either by starting within the treatment and spreading out (Bdtn = 1) or by starting outside and spreading into (Bdnt = 1). This framework allowed us to statistically distinguish the performance of treatments when their influence was localized versus when they interacted with the surrounding untreated landscape. Only the explanatory variables that were statistically significant at 5% or better were included in the final regression models. The models showed good model fits with Nagelkerke’s pseudo-R² of 0.740 and 0.630 for AB and TC, respectively.

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Table 3. The estimated regression model for total cost of fuel treatment and timber loss.

https://doi.org/10.1371/journal.pone.0342049.t003

Obviously, AB expanded as the fire continued to burn. For one additional hour of burning, ceteris paribus, area burned on average increased by 16.0% of the total area burned at the beginning of the hour (Table 2). TC showed a similar pattern of correlations with fire duration (h), with a 11.9% increase for each additional hour of burning (Table 3). Both AB and TC increased with longer delays in fire occurrence after treatment (τ). However, timber volume (Bm) had opposite impacts on AB and TC—a higher Bm value tended to lower AB but heighten TC (Tables 2 and 3). It is important to note that while the regression coefficient for Bm is small on a per-unit basis, its influence could be substantial given that the variable spans a range of over 300 m³/ha in our dataset.

Before detailing the results for AB and TC, we note that our supplementary regression analyses for FL, FI, CFA, and ROS revealed a similar pattern of treatment effectiveness on AB and TC. The direction and significance of the main explanatory variables—particularly the interactions between treatment option, timber volume (Bm), and time since treatment (τ)—were consistent across all models. The full statistical results for these corroborating analyses are provided in S9–S12 Tables, and their visual trends are shown in S3 and S4 Figs.

Effects of fuel treatments on area burned

The effectiveness of fuel treatments in reducing AB depended upon many factors. AB was significantly correlated with both the fuel treatment options and their interactions with other explanatory variables representing whether a fire spread out of or into the treatment area (Bdtn or Bdnt), how much timber was available (Bm), how far away the ignition location was from the treatment boundary (d), and how soon a fire occurred after treatment (τ).

The sums of coefficients associated with Bdtn and PB×Bdtn, Bdtn and TFB×Bdtn, Bdnt and PB×Bdnt, and Bdnt and TFB×Bdnt were all positive (Table 2). Consistent with expectations, the effectiveness of both PB and TFB declined when a fire burned across the treatment boundary. Our models further allowed us to quantify this reduction: the positive interaction terms (e.g., PB×Bdtn, TFB×Bdtn) show the specific penalty to effectiveness at the landscape level compared to the site level and reveal how this penalty varies by treatment option. The effectiveness of PB and TFB increased as d decreased (closer to the center of the treatment area on either side of the treatment boundary) given the positive coefficients associated with PB × d and TFB × d. TFB was less responsive to a change in d than PB.

An increase in Bm reduced AB and such an effect was more profound for TFB than for PB as indicated by the negative coefficient associated with TFB × Bm. The influence of Bm on treatment effectiveness also varied with d, τ, Bdtn, or Bdnt. Where a fire started and stayed in the treatment area (d < 0 and Bdtn = 0), ceteris paribus, PB was effective as long as Bm < 249.3 m³/ha and TFB was effective as long as Bm > 46.8 m³/ha. The effectiveness of PB or TFB increased as d decreased (closer to the center of the treatment area) or τ increased (Fig 3a-f). The positive coefficient associated with τ implies that AB increased over time without treatment; however, PB and TFB were more effective than NT given the negative coefficients of PB × τ and TFB × τ. For a 1-year delay in fire occurrence, AB increased by 15.2%, 11.9%, and 8.1% under NT, PB, and TFB, respectively (Table 2).

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Fig 3. Effects of fuel treatments on area burned.

Subplots are organized by columns representing site-level effectiveness (left; d < 0 and Bdtn = 0), landscape-level effectiveness (spreading out) (center; d < 0 and Bdtn = 1), and landscape-level effectiveness (encroaching fire) (right; d > 0 and Bdnt = 1). NT = non-treatment, PB = prescribed burning, and TFB = thinning from below. Y denotes area burned. The vertical axis represents the log-ratio of area burned between the compared treatment options. The shaded gray area below the horizontal line placed at the zero value of the vertical axis indicates where the treatment is effective in reducing area burned compared to the baseline. d represents the distance of the ignition location from the treatment boundary (d < 0 inside the treatment area, d > 0 outside the treatment area) (km), Bm depicts the volume of timber prior to fuel treatment (m³/ha), and τ indicates the number of years after treatment when the fire occurs.

https://doi.org/10.1371/journal.pone.0342049.g003

Overall, both PB and TFB were effective in reducing AB at both the site and landscape levels, although their effectiveness was lower at the landscape level. The effectiveness of TFB was positively correlated with Bm whereas that of PB was negatively correlated with Bm (Fig 3a-f). The effectiveness of PB and TFB was more evident where there was a longer delay in fire occurrence after treatment (larger τ) (Fig 3a-f) or when a fire starting in the non-treatment area burned across the treatment boundary (d > 0 and Bdnt = 1) (Fig 3c, 3f). TFB was more effective than PB as τ, d, and Bm increased or when a fire started in the treatment area and spread into the non-treatment area (d < 0 and Bdtn = 1) (Table 2, Fig 3g-i).

Effects of fuel treatments on total cost

Likewise, we found complex relationships between fuel treatments and TC. Although the fuel treatments incurred costs, they could reduce timber losses by reducing fire risks and severity. The effect of a fuel treatment on TC also depended on not only the treatment itself but also its interactions with the crossing of the treatment boundary by a fire (Bdtn or Bdnt), quantity of timber prior to treatment (Bm), distance of the ignition location from the treatment boundary (d), and delay in fire occurrence after treatment (τ).

The sums of coefficients associated with Bdtn and PB×Bdtn, Bdtn and TFB×Bdtn, Bdnt and PB×Bdnt, and Bdnt and TFB×Bdnt were all positive (Table 3). This observation indicates that PB and TFB were less effective in mitigating TC at the landscape level than at the site level. The negative coefficient associated with TFB×Bdtn (TFB×Bdnt) was smaller than that with PB×Bdtn (PB×Bdnt). Thus, TFB was more effective than PB where a fire burned across the treatment boundary regardless of its ignition location (i.e., at the landscape level).

The coefficients associated with PB × Bm and TFB × Bm were negative (Table 3), implying the effectiveness of PB and TFB (relative to NT) improved as Bm increased. When a fire started and stayed in the treatment area (d < 0 and Bdtn = 0), PB and TFB were effective in reducing total cost where Bm > 748.8 m³/ha and Bm > 615.5 m³/ha, respectively. The minimum Bm threshold at which fuel treatments became effective was 105.3 m³/ha for PB and 147.4 m³/ha for TFB when fires spread from the treatment area to the non-treatment area. When fires spread in the opposite direction—from the non-treatment area to the treatment area—the thresholds were slightly higher: 110.4 m³/ha for PB and 155.9 m³/ha for TFB, respectively. Interestingly, while the effectiveness of PB decreased as d increased (Fig 4a-c), the effectiveness of TFB was independent of d (Fig 4d-f). This advantage of TFB over PB was also more evident with an increase in τ. For a 1-year delay in fire occurrence, total cost increased by 14.3% for the area treated with PB or untreated while it went up by 9.0% for the area treated with TFB (Table 3).

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Fig 4. Effects of fuel treatments on total cost of treatment and timber damage.

Subplots are organized by columns representing site-level effectiveness (left; d < 0 and Bdtn = 0), landscape-level effectiveness (spreading out) (center; d < 0 and Bdtn = 1), and landscape-level effectiveness (encroaching fire) (right; d > 0 and Bdnt = 1). NT = non-treatment, PB = prescribed burning, and TFB = thinning from below. Y denotes total cost. The vertical axis represents the log-ratio of area burned between the compared treatment options. The shaded gray area below the horizontal line placed at the zero value of the vertical axis indicates where the treatment is effective in reducing total cost compared to the baseline. d represents the distance of the ignition location from the treatment boundary (d < 0 inside the treatment area, d > 0 outside the treatment area) (km), Bm depicts the volume of timber prior to fuel treatment (m³/ha), and τ indicates the number of years after treatment when the fire occurs.

https://doi.org/10.1371/journal.pone.0342049.g004

Overall, effectiveness of PB and TFB in mitigating total cost at both site and landscape levels largely depended on the amount of biomass (Bm), and both treatments would be effective with a sufficiently large Bm (Fig 4a-f). TFB outperformed PB with an increase in Bm, d, and τ or at the landscape level (Table 3, Fig 4g-i).

Effectiveness by biomass level

To a large extent, whether PB and TFB were effective in reducing AB or TC depended on the amount of biomass or timber (Bm). However, Bm had a different effect on AB than on TC. As Bm increased, AB decreased due to a larger proportion of forestland relative to grassland and shrubland (fires tended to spread faster in grassland or shrubland than in forestland), while TC rose due to the higher timber volume that could potentially be lost to a fire. TFB became more effective than PB or NT in mitigating both AB and TC with an increase in Bm.

To achieve site-level effectiveness in reducing AB, Bm had to be below 249.3 m³/ha for PB and above 46.8 m³/ha for TFB. However, to attain effectiveness at the landscape level, the required maximum Bm for PB decreased, and the minimum Bm for TFB increased. While the Bm required for site-level effectiveness in reducing TC was relatively high, it dropped significantly once fires spread between treatment and non-treatment areas. Specifically, the minimum Bm threshold for effective cost mitigation was 105.3 m³/ha for PB and 147.4 m³/ha for TFB when fire spread from the treatment area to the non-treatment area. When fires spread in the opposite direction, the thresholds were slightly higher, 110.4 m³/ha for PB and 155.9 m³/ha for TFB, respectively. By contrast, the mean of Bm at the county level was 58.2 m³/ha with a range of 33.9–99.5 m³/ha across the 43 forest counties in East Texas, but Bm at the forest stand level was higher with an estimated mean of 118.04 m³/ha [49]. This gap in Bm suggests that, across most timberlands in our study area (where mean Bm = 58.2 m³/ha), both PB and TFB are likely to reduce AB. However, because treatment costs are high—especially for TFB—only a small subset of high‐volume stands (those exceeding the Bm thresholds) can be cost-effectively treated with these methods. Meanwhile, these timberlands also provide significant non-timber values ranging from carbon to wildlife habitat that are susceptible to wildfire as well [103,104]. If these non-timber benefits are accounted for, then PB and TFB may become more justifiable economically.

This finding is directly supported by our fire behavior analysis. The reduction in TC is driven by reduced timber loss, which was estimated by the FVS-FFE that defines timber loss and tree mortality as a function of fire severity. Our supplementary regression model for fireline intensity (S10 Table) confirms that the treatments were also effective at reducing fire intensity under high-biomass conditions. These findings suggest that fuel treatments lower fire intensity, reducing economic damage (timber loss).

Effectiveness at the landscape level

Our results show that PB and TFB were less effective in reducing AB or TC at the landscape level than at the site level. This outcome was largely because fires burned across the treatment boundary. To lessen the chance for a fire to cross the treatment boundary, treatment area should be relatively large and/or placed in the location of high fire risk. It is beyond the scope of this study to explore the optimum size and locations of treatment areas [105]. Nevertheless, as described above, our findings reveal that TFB is a better choice than PB when there is little knowledge about where fires would occur, and that PB and TFB are effective even when a fire burns across the treatment boundary as long as the timber volume reaches its required threshold. Additionally, because large fires are more likely to burn across treatment boundaries, PB and TFB tend to be effective to mitigate AB and TC of these fires. This advantage is likely driven by TFB’s direct impact on forest structure. By removing ladder fuels, TFB is more effective than PB at reducing crown fire activity, especially in high-biomass stands (S11 Table), thereby limiting a primary driver of large-scale fire spread. As our findings in fireline intensity (S10 Table) indicates, PB and TFB can be effective in reducing burning severity, thus mitigating severe ecological impacts, as consistently supported by the literature [25,32,106].

It is challenging to precisely predict where a fire will hit. Our result shows that the effectiveness of TFB in mitigating AB and TC was less sensitive to fire ignition location (d) than that of PB. Hence, when it is highly uncertain about where a fire will start, TFB tends to be a better treatment option than PB. This pattern becomes more pronounced as timber volume (Bm) or fire occurrence year after treatment (τ) increases or when a fire burns at the landscape level (Bdtn = 1 or Bdnt = 1). However, we used a simplified spatial configuration by uniformly placing treatments at the center of each representative fuel landscape (RFL) and then simulating randomly distributed ignition points around the treatment boundary to assess marginal distance effects. While this controlled framework provided a consistent way to examine how effectiveness changes with ignition proximity, it does not capture the full range of real-world ignition scenarios, terrain constraints, or budget- and access-driven placement of treatments. Future studies should therefore incorporate spatial optimization of treatment locations, realistic implementation constraints, and a broader suite of ignition patterns to better reflect operational conditions.

Although this study emphasizes AB and TC, our modeling results for all metrics (AB, TC, FL, FI, CFA, and ROC) consistently reveal that PB and TFB become less effective when a fire burns across treatment boundaries, either from the treated area to the untreated area or from the opposite direction. This suggests that PB and TFB are less effective in mitigating area burned, fire intensity, and timber loss at the landscape level than at the site level.

Effectiveness duration

Our results indicate that the relative effectiveness of fuel treatments, when compared to no treatment, grew as the time since treatment (τ) increased. This may seem counterintuitive, as vegetation and fuel loads regenerate over time. The model explains this dynamic through the interaction between the main effect of time and the treatment interaction terms. The main coefficient for τ is positive (Tables 2 and 3), confirming that in an untreated stand, AB and TC increase each year due to fuel accumulation. However, the negative coefficients for the interaction terms (PB × τ and TFB × τ) show that this increase is significantly dampened in treated areas. In other words, while fire risk increases in treated areas over time, this increase is at a much slower pace than in untreated areas. Consequently, the difference between treated and untreated areas widens over the 1–3 year period we studied, making the treatment appear more effective relative to NT in year 3 than in year 1. For a 1-year delay, TFB was 30% and 27% more effective in mitigating AB and TC than PB, respectively. This finding aligns with previous work demonstrating that TFB retains its effectiveness longer than PB [9,107].

The longer duration of TFB’s effectiveness is rooted in its impact on forest structure. By mechanically removing ladder fuels and increasing the distance between the ground and tree canopies, TFB fundamentally alters the pathways for fire to transition from the surface to the crown. These structural changes are far more persistent than the reduction of fine surface fuels achieved by PB [108,109]. Our supplementary regression analysis confirms that TFB provides a sustained mitigation of crown fire activity (S11 Table). This reduction in crown fire potential is strongly correlated with a smaller final area burned, as it limits fire spotting and the potential for rapid, uncontrollable fire growth. PB, however, is generally less effective at reducing crown bulk density and its impact on smaller surface fuels is relatively short-lived, with effectiveness generally considered highest in the first few years before fine fuels re-accumulate.

Implication for fuel treatment operation

Our findings offer several suggestions for designing and implementing fuel treatments under real-world constraints in the southern United States. First, forest managers need to target high-biomass stands for cost effectiveness. Since both PB and TFB require minimum timber‐volume thresholds (105.3 m³/ha for PB; 147.4 m³/ha for TFB) to be economically justified at the landscape level, managers should prioritize treatments on stands exceeding these values. In regions where mean biomass is below these thresholds, PB may still effectively reduce area burned but offers limited cost savings unless non-timber benefits (e.g., carbon sequestration, wildlife habitat) are also quantified and credited in benefit–cost analyses.

Second, forest managers should prioritize treatment placement in areas with high-risk of fire. Because landscape-level effectiveness depends on intercepting large fire perimeters, treatments should be concentrated in locations where large wildfires are most likely or historically frequent. By targeting these “hot spot” zones, managers can maximize the chance that treatments will interrupt fire spread at scale—thereby improving returns on investment in both AB and TC reduction [15,24].

Third, forest managers can benefit from implementing hybrid treatment schedules. Combining an initial thinning treatment to remove ladder and canopy fuels with periodic PB can harness the structural longevity of TFB while using PB to curb fine-fuel accumulation at a lower ongoing cost. Re-treatment intervals should align with site-specific vegetation growth rates and fuel accumulation dynamics to sustain mitigation benefits over multiple years.

Limitations and direction of future work

This study has several limitations, which suggest needs and directions for future research. We group these into three main areas: simulation framework, analytical scope and metrics, and economic simplifications.

Our simulation results are subject to the inherent assumptions of the FARSITE model, such as fuel homogeneity for each fuel type/model and the absence of fire-atmosphere interactions [77]. These assumptions may oversimplify real-world fuel variations and ignore the feedback effect of a fire on local weather conditions. Furthermore, we used a fixed circular treatment design rather than exploring multi-dimensional variations in treatment size, shape, and placement [22,110,111]. Future research can utilize optimization tools like the Treatment Optimization Model (TOM) to evaluate more complex spatial treatment patterns [24]. As this study focused on high-risk fire weather, future work can also consider a broader range of weather scenarios.

The analytical metrics of this study were primarily area burned and the total cost of fuel treatment and timber loss and, to a less extent, fire intensity. Future research can include more in-depth analysis of fuel treatment effects on fire severity and consider non-timber damages (e.g., infrastructure, housing, ecosystem services, and human health). While our use of 10 RFLs allowed for a statistically sound comparison of site- and landscape-level effectiveness, expanding this to larger or other ecosystems or accounting for spatial correlations between RFLs remains another area for future work. Additionally, as our study covered only a post-treatment period of three years, longer-term analysis is needed to identify when treatment effectiveness eventually fades out as fuels re-accumulate.

In estimating the total cost, we employed average per-hectare treatment costs and assumed the total loss of all mortality-affected timber without accounting for potential salvage revenue. In reality, treatment costs vary with stand structures and terrain conditions. Fuel treatments can also create suppression opportunities and lower suppression costs by reducing fire intensity [112,113]. Improving cost and damage estimations and linking treatments to fire suppression benefits warrant further investigation.