Abstract
Fire has influenced Sierra Nevada ecosystems for millennia; however, increasing wildfire size and frequency may yield unforeseen consequences on wildlife populations and their distribution. Foothill yellow-legged frogs Rana boylii have declined in portions of their range and are considered a species of conservation concern. We surveyed streams for foothill yellow-legged frogs in and near the 2021 Dixie Fire footprint using double-observer visual encounter surveys that incorporated time-to-detection methods and used structural causal modeling to improve post-fire inference while lacking prefire data. We found that foothill yellow-legged frog probability of occurrence was 4.93 (95% equal-tailed interval = 0.52–160) times higher outside the footprint of the Dixie Fire than within it, though probability of occurrence was generally low within our sampling frame (ψunburned = 0.21 [0.08–0.49]; ψburned = 0.05 [0.002–0.28]). Measured environmental characteristics, however, were similar within and outside the fire footprint, and observed occupancy patterns might reflect the recent historical distribution of the frogs. Our study emphasizes the importance of site-specific pre-disturbance data when attempting to evaluate the causal effects of disturbances on wildlife. Although it remains to be seen how this species will fare in an increasingly frequent and intense fire regime, foothill yellow-legged frogs may tolerate some level of fire disturbance.
Introduction
Structural causal modeling (SCM) has emerged as a useful tool for drawing causal inference from observational data (Pearl 1995; Arif and MacNeil 2023). The benefits of SCM are especially profound in fields like sociology, economics, and medicine, where manipulative experiments are impossible, unethical, or both (Laubach et al. 2021; Arif and MacNeil 2023; Stewart et al. 2023). Ecology and resource management face similar difficulties to these fields, either because the rarity of organisms makes manipulation unethical or because the scale at which processes operate makes manipulation impossible (Laubach et al. 2021; Arif and MacNeil 2023).
Structural causal modeling is useful at multiple stages of ecological investigation. Investigator knowledge can be explicitly used to construct a directed acyclic graph (DAG) of the system, which represents hypotheses about causal relationships in the system of interest, prior to investigation to identify potential confounding variables that, if unaccounted for, might result in biased inference (Pearl 1995; Arif and MacNeil 2023). Investigators can then use the DAG as a guide for which variables to measure in the field to obtain minimally biased inference (Arif and MacNeil 2022; Arif and Massey 2023). Directed acyclic graphs are also, and perhaps more generally, used to guide development of the statistical model to generate minimally biased inference when analyzing data (Laubach et al. 2021; Stewart et al. 2023). Thus, the use of SCM is independent of the statistical model (distribution families, link functions, functional relationships, etc.) chosen for analysis and of the sampled data (Pearl 1995; Huntington-Klein 2022). Instead, SCM is a way to explicitly represent hypothesized causal mechanisms operating in the system of interest and identify whether and how it is possible to generate minimally biased estimates of specific causal relationships from observational data (Pearl 1995; Huntington-Klein 2022; Arif and MacNeil 2023).
The ability to estimate causal relationships from observational data greatly benefits many questions in ecology and resource management. For example, wildfires can have profound effects on human and wildlife populations. In California, the frequency and total area burned by wildfires have increased between 2000 and 2019 compared to the previous 80 years (Li and Banerjee 2021). This has been driven, in part, by massive wildfires, such as the Dixie Fire that burned 389,837 ha in 2021. Projected climate changes in California include increased precipitation volatility (Swain et al., 2018), delayed onset of autumn precipitation (Goss et al. 2020; Luković et al. 2021), and increased temperatures (Goss et al. 2020), which increase the risk of extreme wildfires (Goss et al. 2020; Swain 2021; MacDonald et al. 2023). Understanding the effects of wildfire on wildlife is therefore more urgent than ever. Before-After-Control-Impact (BACI) studies (Stewart-Oaten et al. 1986; Underwood 1992; Popescu et al. 2012; Chevalier et al. 2019) are standard for assessing large scale ecological processes from quasi-experimental and observational data. Determining the effects of wildfire and other disturbances, however, can be difficult because prior information about where and when they will occur is lacking; therefore, establishing baseline information prior to disturbance is difficult.
Much of what is known about amphibian responses to wildfire comes from a sequence of wildfires in and near Glacier National Park from the late 1980s to early 2000s that occurred in portions of areas where long-term monitoring was ongoing (Hossack and Corn 2007; Hossack et al. 2013) and BACI studies possible. In the short-term, wildfire did not affect wetland occupancy of pond-breeding amphibians (long-toed salamanders Ambystoma macrodactylum or Columbia spotted frogs Rana luteiventris; Hossack and Corn 2007), although the occurrence of both species declined 7–21 years following wildfire in areas affected by high-severity burns (Hossack et al. 2013). Western toads Anaxyrus boreas often colonized previously unoccupied wetlands the year after they burned (Hossack and Corn 2007; Hossack et al. 2013). Rocky Mountain tailed frog Ascaphus montanus larvae decreased in relative abundance in burned headwater streams immediately after wildfire but recovered to pre-burn conditions within 10 years (Hossack et al. 2006; Hossack and Honeycutt 2017). Wildfire affects amphibians in different ways, depending on the species, fire severity, time since the fire occurred, and other ecological contexts.
Foothill yellow-legged frogs Rana boylii (Figure 1; hereafter FYLF) are stream specialists that have declined and are a species of conservation concern in much of their range (U.S. Fish and Wildlife Service 2021). A number of threats to FYLF have been identified, including alteration of stream hydrology and temperature caused by dams (Lind et al. 1996; Kupferberg et al. 2011, 2012; Wheeler et al. 2015; Catenazzi and Kupferberg 2018), habitat loss and alteration (Hayes and Jennings 1988; Kupferberg 1996; Wheeler and Welsh Jr. 2008; Kupferberg et al. 2011), invasive species (Kupferberg 1997a; Paoletti et al. 2011; Adams et al. 2017), contaminants (Sparling and Fellers 2007, 2009), disease (Kupferberg et al. 2009; Adams et al. 2017; Belasen et al. 2024), and altered algal communities (Kupferberg 1997b; Furey et al. 2014; Catenazzi and Kupferberg 2018). Although each of these threats can act alone to reduce abundance or extirpate FYLF (e.g., poorly timed releases from dams can scour streams and eliminate subadult life stages), they often interact to cause greater harm than additive effects alone (Furey et al. 2014; Adams et al. 2017). Despite this extensive knowledge about the biology of and threats to FYLF, little is known about their response to wildfire.
A subadult foothill yellow-legged frog Rana boylii, Colusa County, California, 2007. U.S. Geological Survey photograph by David Dimitrie.
A subadult foothill yellow-legged frog Rana boylii, Colusa County, California, 2007. U.S. Geological Survey photograph by David Dimitrie.
The complexity of the effects of wildfire on stream conditions makes predicting wildfire effects on FYLF difficult. For example, FYLF could benefit from fire if it opens the canopy and improves stream conditions for algal growth and FYLF larval development (Figure 2). On the other hand, siltation of streams from the removal of vegetation by wildfire could eliminate breeding sites and entire populations (Figure 2). Thus, examining the effects of wildfire on stream conditions and FYLF is an important consideration for the conservation of FYLF in a changing climate.
Directed acyclic graph (DAG) showing causal pathways for foothill yellow-legged frog Rana boylii occurrence in the year following wildfire in northeastern California, 2022. Colors: yellow = latent (unobserved) variable; indigo = confounding variable (backdoor pathway) between wildfire and probability of occurrence following wildfire controlled for in the model; green = exposure of interest; aqua = hypothesized indirect effects (mediators) of the effect of the exposure on the outcome; blue = outcome of interest. Psi = probability of occurrence of foothill yellow-legged frogs; CC = canopy cover; before = before fire; after = after fire. We have omitted other causes of foothill yellow-legged frog occurrence for clarity.
Directed acyclic graph (DAG) showing causal pathways for foothill yellow-legged frog Rana boylii occurrence in the year following wildfire in northeastern California, 2022. Colors: yellow = latent (unobserved) variable; indigo = confounding variable (backdoor pathway) between wildfire and probability of occurrence following wildfire controlled for in the model; green = exposure of interest; aqua = hypothesized indirect effects (mediators) of the effect of the exposure on the outcome; blue = outcome of interest. Psi = probability of occurrence of foothill yellow-legged frogs; CC = canopy cover; before = before fire; after = after fire. We have omitted other causes of foothill yellow-legged frog occurrence for clarity.
The goal of our study was to evaluate the effects of wildfire on FYLF distribution and habitat. Our specific objectives were to (1) compare FYLF habitat and stream characteristics within the footprint of the Dixie Fire to those outside the footprint of the Dixie Fire; and (2) estimate the effects of the Dixie Fire on FYLF occurrence. To achieve Objective (2), we used SCM as a framework to guide the development of our model and understand limits to our inference in four ways. First, we used SCM to demonstrate the potential pathways by which wildfire might affect FYLF occupancy. Second, SCM guided our inclusion of potential confounding variables in our assessment of the effects of wildfire on the species. Third, SCM allowed us to explicitly identify limits to inference caused by lack of information from before the fire. Fourth, we used SCM to guide future studies seeking to use post-disturbance information to draw inferences about effects on wildlife.
Study Site
We conducted our study in the footprint of the Dixie Fire and adjacent areas within the distributional and elevational range of FYLF, based on the U.S. Fish and Wildlife Service range polygon for the species, on public lands in Plumas, Lassen, Butte, Tehama, and Shasta counties, California (Figure 3). The study area is predominantly within the lower montane ecotone of the Sierra Nevada, which is characterized by ponderosa pine Pinus ponderosa, Jeffrey pine P. jeffreyi, white fir Abies concolor, and incense cedar Calocedrus decurrens in the uplands with white alder Alnus rhombifolia and willows Salix spp. along the riparian corridors. We selected sampling locations using a balanced dual-frame Generalized Random Tessellation-Stratified sample (Stevens and Olsen 2004) of pre-defined stream segments (hereafter sites) based on the National Hydrography Dataset (U.S. Geological Survey 2019) that represented recent (since 2000) FYLF records (California Department of Fish and Wildlife 2022) and those of unknown FYLF occurrence status that were either within the footprint of the Dixie Fire or outside, but within 10 km of, the perimeter of the Dixie Fire. This sampling frame resulted in 10 sites in burned areas with recent FYLF observations (with five alternative sites), 20 sites in unburned areas with recent FYLF observations (with 20 alternative sites), 15 sites in burned areas without recent FYLF observations (with 15 alternative sites), and 15 sites in unburned areas without recent FYLF observations (with 15 alternative sites). We manually apportioned the number of sites within these four strata based on the number available in each stratum to reduce the clustering of sampling sites that could be caused by geographic clustering of recent frog observations in the study area. We surveyed alternative sites if the primary sites could not be surveyed for a variety of reasons, including inaccessible roads, completely dry streams, and health and safety risks for surveyors.
Map indicating the status of foothill yellow-legged frog Rana boylii (FYLF) surveys in 2022 in and near the footprint of the 2021 Dixie Fire, California, USA. Note that areas adjacent to the Dixie Fire but burned in 2020 were not included in our sampling frame.
Map indicating the status of foothill yellow-legged frog Rana boylii (FYLF) surveys in 2022 in and near the footprint of the 2021 Dixie Fire, California, USA. Note that areas adjacent to the Dixie Fire but burned in 2020 were not included in our sampling frame.
Methods
Field methods
We visited 114 stream reaches in the study area in summer 2022 and conducted visual encounter surveys at 43 of them. The remaining 71 sites were dry (n = 37) or inaccessible (n = 34). A pair of trained U.S. Geological Survey Biological Science Technicians conducted visual encounter surveys using independent double-observer methods, supplemented with time-to-detection techniques (Garrard et al. 2008; Halstead et al. 2018), to estimate detection probabilities (three sites were surveyed only once). Briefly, technicians walked slowly upstream and independently counted the number of each life stage of each amphibian or reptile species at each stream reach. At sites where the average stream width was <3 m, the second technician followed behind the first technician as far as possible while staying within visual contact (for safety reasons) to allow for any animals disturbed by the first technician to reset and become available for detection. At sites where the average stream width was ≥3 m, the technicians walked along opposite shores of the stream at the same time and only counted animals observed on their half of the stream. Each technician logged the location and time of detection of the first FYLF of any life stage encountered during their survey. Technicians evaluated several site characteristics relevant to FYLF, including stream flow velocity, average stream width and maximum depth, canopy cover (shade), and substrate size and characteristics. The technicians also recorded environmental conditions by measuring air and water temperatures and estimating wind speed and cloud cover upon observation of the first FYLF or at the end of the survey, whichever came first. Site characteristics and data used in this study are available in Table 1 or Kleeman et al. (2024).
Environmental and survey characteristics of sites surveyed for foothill yellow-legged frogs Rana boylii in and near the Dixie Fire in northeastern California, 2022. Site indicates the last six digits of the HUC-12 watershed (the first six digits for all HUC-12 watersheds is 180201) followed by sequential numbers for different sites within the same HUC-12 watershed.

Analytical methods
We used multiple methods to compare FYLF habitat components within and outside the footprint of the Dixie Fire. For continuous variables, we used a Bayesian implementation of a t-test with unequal variances to compare stream characteristics within and outside the footprint of the Dixie Fire, whereas for categorical variables, we used a Bayesian implementation of a binomial test to test whether the probability sites exhibited different characteristics varied between burned and unburned areas. For both models, we selected priors to be vague (Supplemental Material Table T1). We ran each model on five independent chains of 2,000 iterations each after a burn-in period of 2,000 iterations in R version 4.1.3 (R Core Team 2024) using Nimble version 1.1.0 (de Valpine et al. 2017, 2022). We assessed convergence by examining history plots and found no evidence for lack of convergence (all history plots appeared well-mixed) and examination of the statistic (all
< 1.02; Gelman and Rubin 1992; Brooks and Gelman 1998). The minimum effective sample size across all monitored parameters in all models was 1,724. Prior distributions, posterior distribution summaries, convergence diagnostics, and effective sample sizes for these models can be found in Supplemental Material Table T1.
Because a major goal of our study was to evaluate evidence for a causal effect of wildfire on the occurrence of FYLF in the year following the wildfire, we used SCM to guide construction of our occupancy model (Arif and MacNeil 2023; Stewart et al. 2023). Specifically, we constructed a DAG as a conceptual model of our understanding of the effects of wildfire on FYLF occurrence to make our assumptions about the effects of wildfire on FYLF explicit and attempt to close any confounding pathways and thereby avoid misleading inference (Figure 2; Pearl 1995; Laubach et al. 2021; Stewart et al. 2023). Two paths in the DAG are of primary concern. First, the backdoor path “wildfire <- drought -> water availability -> FYLF occurrence after fire (ψafter)” needs to be closed to minimize bias when estimating the effect of wildfire on ψafter. We closed this path by excluding stream reaches that were observed to be completely dry, and therefore inhospitable to FYLF, from our sample under the assumption that if water was present at the time of sampling (during mid–late summer during an extreme drought), then enough water was available for FYLF to occur. This effectively removes the relevant variation in water availability from this path and closes it (Huntington-Klein 2022). The second biasing path, “wildfire <- canopy cover before fire -> FYLF occurrence before fire [ψbefore] -> ψafter,” is based on pre-fire conditions: namely, that canopy cover prior to the fire could be a cause for both propensity for wildfire (higher canopy cover represents more fuel) and a cause of FYLF occurrence before the fire (canopy closure could reduce suitability of stream reaches for FYLF by reducing stream temperature and limiting algal resources for larvae; Furey et al. 2014; Hayes et al. 2016; Catenazzi and Kupferberg 2018). We closed this backdoor pathway between wildfire and FYLF occurrence after the fire by deriving pre-fire canopy cover based on satellite imagery prior to the Dixie Fire and including it as a variable in our model.
Based on analysis of the DAG, we constructed a multiple survey time-to-detection occupancy model (Garrard et al. 2008; Halstead et al. 2018, 2021; Medina-Romero et al. 2019; Henry et al. 2020). We did not construct a DAG for the detection component of the model because we did not incorporate covariates in that part of the model and because the structure of the detection component does not generally induce bias in the occurrence component of the model (Stewart et al. 2023). We used a means parameterization to estimate mean occupancy of FYLF in recently burned and nearby unburned areas. Because we lacked detailed information about site conditions prior to the fire, were interested in the total effect of fire, and had a limited sample size with relatively few detections, we did not include potential mediators, such as substrate or canopy cover following the fire, in our model. We checked for conditional dependencies between estimated canopy cover prior to the fire, whether a site was burned, and whether we detected FYLF at a site, and no Pearson correlation coefficients were strong nor statistically significant (ρcc_burn = 0.21 [95% confidence interval = −0.10–0.48]; ρcc_det = −0.19 [-0.46–0.12]; ρburn_det = −0.27 [−0.52–0.04]). Nonetheless, because canopy cover prior to the fire had weak relationships with the burn status and detection status of a site in the predicted directions, we included an additive effect (i.e., same effect for burned and unburned sites) of canopy cover prior to the fire in our model to account for any potential confounding caused by pre-fire canopy cover. To account for site heterogeneity in detection rate induced by, for example, species abundance or site conditions, we included a log-linear random effect of site on detection rate. We used vague priors for all model parameters (Table 2) and evaluated fit with a χ2 goodness-of-fit test. Model code to reproduce the analysis is available on the U.S. Geological Survey Git Repository (Halstead et al. 2024). We ran each model on five independent chains of 2,000,000 iterations each after a burn-in period of 20,000 iterations in R version 4.1.3 (R Core Team 2024) using Nimble version 1.1.0 (de Valpine et al. 2017, 2022). We thinned output by a factor of 100, basing inference on 100,000 samples from the posterior distribution. We assessed convergence by examining history plots and found no evidence for lack of convergence (all history plots appeared well-mixed) and examination of the statistic (all
< 1.03; Gelman and Rubin 1992; Brooks and Gelman 1998). The minimum effective sample size across all monitored parameters was 1,821 (Table 2). Unless otherwise indicated, we report posterior medians and 95% equal-tailed intervals (0.025–0.975 quantile of the posterior distribution) for the time-to-detection occupancy analysis.
Results
Environmental characteristics
The probability a visited site could be sampled in unburned areas was 0.40 (95% equal-tailed interval = 0.30–0.52) and in burned areas was 0.34 (0.21–0.48), a difference of 0.06 (−0.11–0.24). Post-fire attributes of unburned and burned sites were similar. Mean elevation of unburned sites was 1,224 m (1,065–1,385 m) and of burned sites was 1,323 m (1,136–1,510 m), a difference of −99 m (−344–147 m; Table 1). Mean canopy cover in unburned sites was 43% (32–53%) and in burned sites was 36% (21–50%), a difference of 7% (−11–25%; Table 1). Mean water temperature in unburned (16.3°C [14.8–17.8°C]) and burned (16.3°C [13.9–18.7°C]) sites was nearly identical, with a difference of 0.0°C (−2.8–2.8°C; Table 1). The probability a site was dominated by silty substrates in the unburned area (0.13 [0.04–0.27]) was lower than in the burned area (0.29 [0.11–0.53]; a difference of −0.16 [−0.42–0.07]; Table 1). The probability the dominant substrate was silt was therefore 2.8 (0.61–14) times higher in burned than unburned sites.
Occupancy
We detected FYLF in eight of 83 surveys at five of 43 sampled sites; all FYLF detections were at sites that were near recent historical records and unburned. The time-to-detection occupancy model provided a good fit to the data (Bayesian P-value = 0.719). Probability of occurrence in unburned sites was 0.21 (0.08–0.49) and in burned sites was 0.05 (0.002–0.28; a difference of 0.14 [−0.09–0.42]; Table 2; Figure 4). Occurrence in unburned sites was therefore 4.93 (0.52–160) times higher than in sites that were burned. The estimated mean time to first detection was 13.3 (3.98–66.2) min. (Table 2), which resulted in a detection probability of 0.85 (0.29–>0.99) for a single survey at our mean survey duration of 24 min (Figure 5). Of the 43 sampled sites, 6 (5–14; Table 2) were estimated to be occupied. The posterior probability of occurrence for sites without detections was <0.21 for all sites and varied as a function of canopy cover prior to the fire, burn status, number of surveys, and survey duration.
Probability of occurrence of foothill yellow-legged frogs Rana boylii based on burn status (burned = burned in Dixie Fire in 2021; unburned = not burned by Dixie Fire) in northeastern California, USA, 2022. Shapes represent posterior probability densities, points represent posterior medians, and vertical lines represent 95% equal-tailed intervals.
Probability of occurrence of foothill yellow-legged frogs Rana boylii based on burn status (burned = burned in Dixie Fire in 2021; unburned = not burned by Dixie Fire) in northeastern California, USA, 2022. Shapes represent posterior probability densities, points represent posterior medians, and vertical lines represent 95% equal-tailed intervals.
Probability of detecting foothill yellow-legged frogs Rana boylii using visual encounter surveys in an average stream as a function of survey duration based on data collected in northeastern California, USA, 2022. The solid line represents the posterior median and shading represents the posterior density in 0.025 quantile bands; the outermost shading represents the 95% equal-tailed interval. Yellow dashed lines represent median detection probabilities for streams one standard deviation below and above the average stream detection rate.
Probability of detecting foothill yellow-legged frogs Rana boylii using visual encounter surveys in an average stream as a function of survey duration based on data collected in northeastern California, USA, 2022. The solid line represents the posterior median and shading represents the posterior density in 0.025 quantile bands; the outermost shading represents the 95% equal-tailed interval. Yellow dashed lines represent median detection probabilities for streams one standard deviation below and above the average stream detection rate.
Discussion
Our study found that FYLF had a higher probability of occurrence at unburned sites near the 2021 Dixie Fire rather than at sites within the fire’s footprint, although our small number of sampled sites with detections resulted in much uncertainty. Nonetheless, our DAG allowed us to avoid common pitfalls associated with including or excluding covariates that could bias inference (Pearl 1995; Laubach et al. 2021; Arif and MacNeil 2023; Stewart et al. 2023). We controlled for water availability by only including sites that had enough water to survey, and therefore enough water to support a population of FYLF, in our sample. Having information on the FYLF occurrence status of sites prior to the fire as in a BACI design, however, would be a more direct and better control for pre-fire conditions than pre-fire canopy cover, which is unlikely to be perfectly correlated with ψbefore. Although BACI designs (Stewart-Oaten et al. 1986; Underwood 1992; Popescu et al. 2012; Chevalier et al. 2019) are much better suited to controlling for the status of sites prior to a disturbance, we think that explicitly diagramming hypothesized causal pathways and controlling for bias to the extent possible represents an important component of post-disturbance causal inference whether or not the BACI design can be used.
Before-after-control-impact designs are powerful because they allow more direct accounting for potential confounding variables (Arif and MacNeil 2022). For example, if we had known occupancy status of burned and unburned sites before and after the Dixie Fire, we could have further minimized this potential cause of confounding in our analysis because canopy cover, although a potential common cause of wildfire and ψbefore, is further removed from and imperfectly correlated with ψbefore and its causal effects on ψafter. Combining a BACI design with SCM also potentially allows an examination of counterfactual questions (Arif and MacNeil 2022). For example, given our DAG and occupancy data for sites prior to the fire, one could ask “What would the occupancy of FYLF at sites burned in the Dixie Fire have been in 2022, had the Dixie Fire not occurred?” Using SCM and DAGs illustrates (1) why BACI designs provide more powerful means of minimizing bias than studies that lack temporal control (Arif and MacNeil 2022); and (2) what variables we should control for (i.e., include in our model), given the goals of the study (Pearl 1995; Arif and MacNeil 2022, 2023; Stewart et al. 2023).
Given our small number of sites with FYLF detections and lack of pre-fire data, we limited our inferential goal to the total effect of the Dixie Fire on FYLF occurrence. Parsing direct and indirect effects of fire is useful for management, however, and our DAG indicates two primary mechanisms that we hypothesized to affect occurrence of FYLF following wildfire. Fire can reduce canopy cover (Agee 1993) and result in debris flows (Kean et al. 2011), changing stream shading and substrate, both of which affect FYLF occurrence (Borisenko and Hayes 1999; Yarnell 2013). Characteristics of surveyable streams within and outside the footprint of the Dixie Fire, however, did not differ statistically in these or other attributes. We therefore cannot attribute the difference in ψafter, itself not statistically distinguishable from zero, to these characteristics. It is possible that unmeasured variables influenced by the Dixie Fire resulted in lower probability of occurrence within the fire footprint, and the direct “wildfire -> ψafter” path encompasses both direct effects and those caused by unobserved mediators. The distribution of FYLF within the study area prior to the fire was largely unknown, so a comparison of the distribution of the species before and after the fire is not possible. Our results might therefore indicate the distribution of FYLF in the study area both before and after the Dixie Fire, rather than being attributable to the fire itself. Our surveys also occurred in the year following the Dixie Fire, and ecological processes like species colonization or extirpation often take years or decades to achieve a new equilibrium following disturbance. The low precision of our estimate of the effect of the Dixie Fire on ψafter was exacerbated by the overall low probability of occurrence in our study area, which supports the presumed rarity of this FYLF clade (U.S. Fish and Wildlife Service 2021).
Structural causal modeling is a powerful approach to causal inference, but its applications in ecology can be somewhat limited. Although we were able to minimize bias by accounting for known and observable confounding variables, unobserved confounding variables are common in complex systems and many causal relationships in ecology are affected by modifiers (Laubach et al. 2021). In our system, much of the uncertainty in our estimate of the effects of wildfire on FYLF was caused by little knowledge of the distribution of the species prior to the fire and the Dixie Fire occurring near the range limits of the species. Even if we had precise estimates of the effects of wildfire on FYLF occurrence, whether the causal effect in this part of the range would also apply to other populations (e.g., northern coastal populations, which are more secure and inhabit a cooler and moister environment (U.S. Fish and Wildlife Service 2021)) would remain unknown. Pluralistic approaches to causal inference, such as Causal Knowledge Analysis (Grace 2024), might help to build a body of evidence for causal effects in complex systems. Pluralistic approaches, however, generally rely on understanding of mechanisms and are ideally based on multiple studies conducted under different conditions and timescales (Grace 2024). For most rare species, such studies are nonexistent.
Little has been published about the immediate response and short-term effects of fire on FYLF, but we can infer possible outcomes based on the life history of the species. Populations of FYLF may experience low direct mortality from the fire itself because this species is rarely more than a few meters from the edge of streams or rivers (Dodd 2023) and the frogs can quickly retreat to water. All life stages of the frogs could, however, be at risk from other immediate effects of fire and its suppression, such as water temperatures rising beyond their thermal tolerances, ammonium toxicity due to smoke diffusion (Spencer and Hauer 1991), or the toxic effects of misplaced fire retardants (reviewed in Pilliod et al. 2003). Fire-induced environmental alterations such as increased solar radiation caused by loss of riparian canopy could lead to increased algal productivity and higher water temperatures, thereby benefitting FYLF populations through increased breeding success (Catenazzi and Kupferberg 2013) and higher population growth rates (Rose et al. 2023). Our environmental comparisons found no significant differences in canopy cover or water temperatures between sites in burned and unburned areas. The mean water temperatures found at both burned and unburned sites (16.3°C) was similar to the threshold temperature of 16°C above which FYLF probability of occurrence was high in coastal watersheds in northern California (Halstead et al. 2020) and were within the range (16–19°C) with the highest density of breeding female FYLF in the Eel River watershed (Catenazzi and Kupferberg 2013). The lack of differences in canopy cover and water temperatures at our sites suggest that either the severity or spatial pattern of the fire did not greatly alter environmental conditions in sampled stream reaches in the year following the fire.
Increased sedimentation in streams due to accelerated erosion from soil hydrophobicity can occur for years following fires depending on the pattern and severity of precipitation events and snowmelt (reviewed by Pilliod et al. 2003). Pools and slow water areas required for FYLF egg deposition can be entirely filled and interstitial spaces in the streambed that offer refuge for larvae and adults can be smothered by sediment. For example, the Camp Fire of November 2018 burned 62,050 ha including uplands adjacent to the North Fork Feather River. Sediment flows the following spring completely buried two FYLF egg masses along the Cresta Reach of the river and covered other egg masses in the Poe Reach with a layer of sediment (J. Drennan, Kleinfelder, unpublished data). The full effect of sedimentation at sites within the Dixie Fire footprint may become more apparent in years following heavy snowpack (e.g., 214% of normal in April 2023; California Department of Water Resources 2023).
Anecdotal evidence from other large fires indicates that FYLF populations can persist post-fire. Multiple surveys in 2019 for post-metamorphic FYLF on a heavily burned unnamed tributary to the North Fork Feather River found large numbers of adult and juvenile frogs, similar to numbers observed in 2018 prior to the Camp Fire (J. Drennan, Kleinfelder, unpublished data). The Rim Fire burned 104,131 ha in 2013, including Big Humbug Creek in Tuolumne County, California. A brief survey by the U.S. Department of Agriculture Forest Service prior to the fire found low numbers of FYLF in the creek (S. Holdeman, U.S. Department of Agriculture Forest Service, unpublished data), but follow-up surveys in 2021 by the National Park Service found hundreds of juvenile FYLF even though many pools had been impacted by debris flows in the interim (R. Grasso, National Park Service, unpublished data). A small population of FYLF in the Jose Creek basin in Fresno County, California, was subjected to the Creek Fire that burned 153,738 ha in 2020. Frogs persist at the site post-fire in reduced numbers, and they were breeding at least 2 y after the fire even though sedimentation affected many of the breeding pools (P. Kleeman and S. Barnes [U.S. Department of Agriculture Forest Service], unpublished data). The SCU Lightning Complex fire burned 160,508 ha in 2020 in the San Francisco Bay Area, including a 2.5-km reach of Arroyo Hondo that has had yearly FYLF egg mass counts since 2014. The 2020 egg mass count prior to the fire was 73, and the counts for the two subsequent years post-fire were 88 and 64, suggesting the FYLF breeding population largely survived the fire (A. Striegle, San Francisco Public Utilities Commission, unpublished data). On a broader spatial scale in Oregon, Olson and Davis (2009) found no significant difference in FYLF presence where stand-replacing fire occurred within 5 km of occupied sites and those without nearby fire. These observations indicate that FYLF may be resilient to wildfire.
Because our study was near the range limits of FYLF and little was known about their occurrence in much of the study area prior to our surveys, in addition to burn status, we stratified our sample by proximity to recent historical records of FYLF. We detected FYLF at four sites where the U.S. Department of Agriculture Forest Service has been monitoring a population in recent years. The fifth site where we detected FYLF, East Branch of Rock Creek, is downstream of a Sierra Nevada yellow-legged frog Rana sierrae re-introduction site. This species is morphologically and ecologically like FYLF in this region, is similarly a species of conservation concern (U.S. Fish and Wildlife Service 2014), and the two species interbreed here (Peek et al. 2019). The surveyor was not able to catch the frogs for closer examination, but because of their ecological similarities in this region, we included these observations in our analysis. The lack of detections of FYLF in our random stratum further suggests that the patterns we observed might reflect recent historical occupancy of the frogs.
Resource managers often seek to inventory rare species following disturbances. The purpose of our study was to estimate a minimally biased effect of wildfire on FYLF, which is why we used an SCM approach to construct a DAG and from it, an occupancy model. In other circumstances, such as prioritizing where to conduct post-disturbance surveys, an approach based on out-of-sample prediction might be more appropriate (Stewart et al. 2023). In this case, a set of models is evaluated, usually with information criteria or cross-validation procedures, for predictive ability. Although these models can improve prediction, estimates of parameters from these models can be biased, resulting in misleading inference about the magnitude or even direction of causal effects (Pearl 1995; Arif and MacNeil 2023; Stewart et al. 2023). We therefore encourage researchers to explicitly state the purpose of their study and use analytical frameworks that perform well for the stated purpose (Tredennick et al. 2021; Stewart et al. 2023).
We gained efficiency in detection probability by collecting time-to-detection data as part of our double-observer survey protocol. Our single survey detection probability at our mean survey duration of 24 min (0.85 [95% equal-tailed interval = 0.29–>0.99]) was greater than comparable single survey detection probability for Yosemite toads Anaxyrus canorus (p = 0.11 [0.05–0.20]), but less than that for sierran treefrogs Pseudacris sierra (p = 0.96 [0.92–0.98]) or Sierra Nevada yellow-legged frogs (p = 0.95 [0.86–0.99]) in predominantly lentic sites (Halstead et al. 2021). Detection probabilities in Halstead et al. (2021) were based on single-survey time-to-detection data, whereas we used time-to-detection data from two independent observers, which allowed us to estimate site-level heterogeneity in detection probabilities. If unaccounted for, unmodeled site heterogeneity in time-to-detection data biases detection probabilities high (Medina-Romero et al. 2019; Henry et al. 2020). Adding a second time-to-detection survey at most sites allowed us to account for this potential heterogeneity while increasing overall detection probabilities (mean cumulative p for two independent 24-min surveys = 0.97 [0.52–>0.99]). Recording time-to-detection data for focal species during visual encounter surveys is a simple addition that can yield useful information on species detectability. Even if resources allow only a single visit by a single observer to a site, collecting time-to-detection and survey duration data can allow estimation of detection probabilities and correction for imperfect detection in rapid post-disturbance assessments of species status.
Our study documented lower probability of occurrence of foothill yellow-legged frogs in the footprint of the Dixie Fire than outside it, despite similar stream conditions in burned and unburned areas. Although wildfires can affect foothill yellow-legged frogs in myriad ways, we found little evidence to suggest that changes to stream characteristics led to post-fire differences in occurrence. Instead, our findings might represent recent (post-dam) historical distribution patterns prior to the Dixie Fire that persist in the post-fire landscape, despite our attempts to control for such differences. Long-term studies over large spatial scales that allow estimation of occurrence or abundance before and after wildfire in burned and unburned areas are ideal for providing robust inference about the influence of fire on amphibian populations. Structural causal modeling can improve inference whether or not pre-disturbance data exist by suggesting ways to reduce or eliminate potential biases when relying on observational data.
Supplemental Material
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Table S1. Prior distributions and posterior summaries for Bayesian binomial tests and t-tests comparing sites surveyed for foothill yellow-legged frogs Rana boylii in 2022 in areas burned by the 2021 Dixie Fire and in adjacent unburned areas.
Available: https://doi.org/10.3996/JFWM-24-037.S1 (22.8 KB DOCX)
Reference S1. Borisenko AN, Hayes MP. 1999. Status of the foothill yellow-legged frog (Rana boylii) in Oregon. Report of The Nature Conservancy to the U.S. Fish and Wildlife Service, Portland, Oregon.
Available: https://doi.org/10.3996/JFWM-24-037.S2 (5.08 MB PDF)
Reference S2. Hayes MP, Wheeler CA, Lind AJ, Green GA, Macfarlane DC. 2016. Foothill yellow-legged frog conservation assessment in California. Albany, California: United States Department of Agriculture, Forest Service, Pacific Southwest Research Station. General Technical Report PSW-GTR-248.
Available: https://doi.org/10.3996/JFWM-24-037.S3 (3.44 MB PDF)
Reference S3. Olson DH, Davis RJ. 2009. Conservation assessment for the foothill yellow-legged frog (Rana boylii) in Oregon, Version 2.0. Corvallis, Oregon: U.S. Department of Agriculture Forest Service and U.S. Department of Interior Bureau of Land Management Interagency Special Status Species Program Report.
Available: https://doi.org/10.3996/JFWM-24-037.S4 (2.40 MB PDF)
Acknowledgments
We thank M. Bellows, Z. Costa, S. Kruleski, P. Lien, and C. Moss for collecting data associated with this project, and L. Stewart and L. Parker for administrative support. M. Adams and three anonymous reviewers provided feedback that greatly improved this manuscript. This work was supported by the U.S. Fish and Wildlife Service and U.S. Geological Survey Ecosystems Mission Area. All work was carried out under California Department of Fish and Wildlife Scientific Collecting Permit SC-10779 and Institutional Animal Care and Use Committee Protocol WERC-2014-01. This is publication 928 of the U.S. Geological Survey Amphibian Research and Monitoring Initiative.
Any use of trade, product, website, or firm names in this publication is for descriptive purposes only and does not imply endorsement by the U.S. Government.
References
Author notes
Citation: Halstead BJ, Kleeman PM, Rose JP. 2024. Using structural causal modeling to infer the effects of wildfire on Foothill Yellow-legged Frog occurrence. Journal of Fish and Wildlife Management 15(2):xx-xx; e1944-687X. https://doi.org/10.3996/JFWM-24-037