Accounting for misclassification of subspecies provides insights about habitat use and dynamics of the Florida Grasshopper Sparrow in response to fire

,

ABSTRACT.Monitoring populations is critical to understanding habitat use, especially for endangered species and is important for determining the effectiveness of land management strategies.The Florida Grasshopper Sparrow (Ammodramus savannarum floridanus) is a critically endangered non-migratory grassland bird that has been monitored since the 1990s.It resides primarily in dry prairie habitat managed by frequent (2-3 years) prescribed fires.Monitoring is confounded by the presence of the migratory and wintering eastern Grasshopper Sparrow (A. s. pratensis), that has vocal and morphological similarities.These similarities could lead to misclassifications and erroneous conclusions about land management.Our goal was to determine the impact of fires on Florida Grasshopper Sparrow habitat use at two spatial scales, 100 m and 400 m buffers surrounding point count locations, while controlling for the presence of the eastern Grasshopper Sparrow.We combined point count data (1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011), external sources of data (eBird), and Bayesian dynamic occupancy models that accounted for misclassifications to evaluate habitat use and dynamics in response to prescribed fires.The probability of misclassifying a Florida Grasshopper Sparrow peaked in April and then decreased to near zero after May 1.The probability of persistence at point count stations decreased as years-since-fire (maximum of pixels within 400 m buffer) increased and was greatest for recent burns (< 1 year).Seasonality of the most recent burn (i.e., ordinal date of burn for pixels within 100 m buffer) also influenced probability of persistence with Florida Grasshopper Sparrows having greater-than-average persistence when burns occurred during January and July, peaking in early April.The probability of colonization peaked approximately two months after a fire and rapidly decreased to negligible values.This is the first long-term study to examine the effect of prescribed burn on Florida Grasshopper Sparrow occupancy that accounts for the presence of eastern Grasshopper Sparrows.This modeling framework may also provide utility for other species and subspecies that are difficult to distinguish during surveys.

INTRODUCTION
Accurate assessment of populations is important for conservation of species and is often used to determine Endangered or Threatened status (e.g., listed by Endangered Species Act [ESA] and International Union for Conservation of Nature [IUCN]).Population change over time is one of the main criteria for deciding the level of protection needed for the ESA and IUCN.Many different methods exist for monitoring populations, but presence-absence surveys are often used given their logistical ease with typical time and budget constraints, especially when a population is difficult to census.
Surveys for population monitoring of birds and other animals often use indirect means of assessment such as vocalizations or other acoustic cues, as this allows researchers to quickly assess presence or absence of single or multiple species during the breeding season (Gibbs 2000).Surveys conducted using acoustic and visual signals, such as point count surveys for birds, can introduce errors in data from misclassification of species.Misclassification of species can occur when species with vocal similarities vocalize during the same time of year.Surveys also use visual cues, but neither may be reliable when species or subspecies share vocal or morphological characteristics.Training for surveyors may prevent misclassification of species that are easily distinguished in the field, but training may be inadequate when certain identification is impossible.
Two common issues that occur in surveys are counting a species as present when it is actually absent (false positive, type 1) and counting a species as absent when present (false negative, type 2); both can lead to incorrect population estimates (Tyre et al. 2003, McClintock et al. 2010, Farmer et al. 2012).Repeating surveys can reduce false negative rates, however, repeated surveys are likely to increase false positives for less common species via misclassification if a similar but more abundant species is present (Tyre et al. 2003, Gu and Swihart 2004, Miller et al 2012).Such misclassifications lead to overestimates of abundance (Chambert et al. 2016) or occurrence (McClintock et al. 2010), which can also lead to incorrect assumptions about habitat usage, preferences, and management.
Statistical methods for modeling occupancy can improve the accuracy of occurrence estimates and account for errors in surveys (Gu and Swihart 2004).MacKenzie et al. (2002) and Tyre et al. (2003) devised a statistical method to increase the accuracy of occupancy estimations by including a detection probability that accounts for missing observations and non-detection of a species.Conventional occupancy models assume that detecting a species where it is not present is impossible.Royle and Link (2006) extended occupancy models to account for misclassifications and concluded that false positives can overestimate occupancy.Several papers also determined that the effects from misclassifications on occupancy estimates are significant (McClintock et al. 2010, Miller et al. 2011) and that even small errors in misclassification can lead to large estimator biases and incorrect conclusions regarding occupancy (McClintock et al. 2010).
The critically endangered Florida Grasshopper Sparrow (Ammodramus savannarum floridanus) provides an excellent case study to use occupancy models that account for misclassification.
Counts of Florida Grasshopper Sparrow during 1998-2017 suggest that populations declined by 89% at three public sites (Florida Grasshopper Sparrow Working Group, personal communication).Point count surveys that target resident Florida Grasshopper Sparrows are confounded with detections of eastern Grasshopper Sparrow subspecies (A.s. pratensis) that winters in the same dry prairie habitat.These two subspecies are not reliably distinguishable in the field.Male Florida Grasshopper Sparrow begin establishing territories in early March (Vickery 1996), which coincides with the onset of point count surveys.The last round of surveys is completed before the end of July.Eastern Grasshopper Sparrows wintering in the same habitat migrate north in the spring before May and are sometimes singing prior to departure (Hewett Ragheb and Schneider 2017).Thus, potential exists for incorrect identification of Florida Grasshopper Sparrow during early point count surveys, but the severity of this problem is poorly understood.Male Grasshopper Sparrows sing more reliably at the beginning of the breeding season and singing decreases in frequency once nesting occurs (Lohr et al. 2013).Florida Grasshopper Sparrows are, therefore, more likely to be recorded as present on point counts conducted during the early breeding season, even without misidentifications of the wintering eastern subspecies.
An important monitoring goal with the remaining populations of Florida Grasshopper Sparrows is their habitat use relative to prescribed fires used to maintain their preferred dry prairie habitat (Walsh et al. 1995, Shriver et al. 1996, Shriver and Vickery 2001, Delany et al. 2002, Delany et al. 2014, Hewett Ragheb et al. 2019).Responses to prescribed fires, generally analyzed for one to two breeding seasons (max.6 years) have been examined with respect to their timing, which includes both the time between fires and the month, or season, in which those fires occurred (Shriver et al. 1996, Shriver and Vickery 2001, Delany et al. 2002, Perkins et al. 2009).Naturally occurring fire seasons are dormant (Oct-Mar), transition (Apr-Jun), and growing (Jul-Sept) seasons (Platt et al. 2015).Long-term studies on the responses of Florida Grasshopper Sparrows to prescribed fires summarizing multiple years of data are needed to fully address the role that fire plays in determining habitat use.Although numerous studies have examined Florida Grasshopper Sparrow responses to fires, none have investigated the effects of fire at multiple spatial scales and using different fire metrics (minimum, maximum, or mean time since fire) to assess the effects on habitat use.
Using historic point count surveys, and a misclassification modeling framework, we evaluated habitat use over time with respect to fires.We specifically asked if fire seasonality or the time since the last fire influence Florida Grasshopper Sparrow occupancy dynamics, while accounting for the presence of the eastern Grasshopper Sparrow.Our goal was to improve the accuracy of the occupancy population estimates using a Bayesian occupancy modeling framework that can be adapted for use with other species where misidentification is an issue.In addition, using an occupancy model to predict the probability of false positives and false negatives may allow for a more accurate assessment of the population, which aids both state and federal agencies deciding future prescribed fire management goals.

Study site
We gathered point count data for Florida Grasshopper Sparrows from a field site located in Polk and Highlands Counties in Florida, USA (mean center located at 27.647188°N and -81.278268°W):Avon Park Air Force Range (hereafter "Avon Park").Three separate sub-populations of Florida Grasshopper Sparrows occur (Delta/OQ Range = 1224 ha, Charlie/Echo Range = 2991 ha, and Bravo/Foxtrot Range = 382 ha).This property contained areas of Florida dry prairie that are considered the primary habitat of Florida Grasshopper Sparrows, and prior to the steep declines that occurred in the late 1990s and early 2000s, contained one of the largest extant populations (Delany et al. 1999, Pranty andTucker 2006).Florida dry prairie is flat and treeless, dominated by pyrogenic wiregrass (Aristida stricta), shrubs such as saw palmetto (Serenoa repens) and dwarf oak (Quercus minima), and numerous herbaceous forbs.Avon Park also was lightly grazed by cattle at 0.18 cow/calf per ha until 2013 (Rolek et al. 2016).Counts of this population declined from 255 birds in 1998 to 2 in 2012 but increased to 6 by 2019 (Bowman personal communication).Despite this long-term decline, the property remains an important source of habitat and potential habitat for this subspecies' recovery.

Point count surveys
We selected a subset of 173 point count locations from a total of 240 at Avon Park that met our criteria for retention (Fig. 1).Our criteria for retention included locations where surveys were conducted for at least 90% of all possible surveys conducted during 1996-2011, and where Grasshopper Sparrows were detected during at least one occasion.Point count locations within each grid were separated by 300-400 m.Surveyors conducted point counts between 15 March and 8 July during the Florida Grasshopper Sparrow breeding season, and most surveys (95%) occurred within three hours of civil dawn.Point count surveys were five minutes in duration.Ideally, surveyors visited sites three times during each breeding season and observers were alternated at least once per season.We did not truncate Florida Grasshopper Sparrow detections at any distance to maintain consistency among years of study, because most point count surveys did not record distance to detection.Florida Grasshopper Sparrows have high-pitched (~ 8 kHz) songs that are difficult for human listeners to hear at great distances, and previous studies suggest a detection radius of < 200 m (Delany et al. 2013).
Several point count locations were not surveyed during some years or for all repeated visits within some years and we assigned missing values to those instances accounting for 4% (366 of 8304) of the total possible survey occasions.Missing point count data occurred because Avon Park Air Force Range is an active military training facility that requires escorts into high explosive areas which may pose risks to the safety of surveyors, and escorts could not always be obtained for surveys.Bayesian methods (described below) accommodate these missing values well because these values are simulated from the model and do not contribute to the likelihood of parameter estimates.An assumption of our analysis is that sites not surveyed did not impose systematic variation in response values.

Detection data
We used point count survey data and a date threshold to classify Florida Grasshopper Sparrow detections into three categories: (1) no Grasshopper Sparrow detected; (2) Grasshopper Sparrow detected but subspecies uncertain; and (3) Florida Grasshopper Sparrow detected with certainty.We designated a threshold date when nearly all detections (> 99%, Fig. 2) of Eastern Grasshopper Sparrows in Florida had ceased using eBird data (Sullivan et al. 2009) from 1995-2012 from Florida counties where Florida Grasshopper Sparrows are not known to persist by excluding data from Highlands, Okeechobee, Osceola, and Polk counties.By excluding these counties, the eBird data only includes migratory Eastern Grasshopper Sparrows and data excludes the Florida subspecies.We used this threshold to assign certainty of subspecies identification to Florida Grasshopper Sparrows detected after 1 May.In addition to the date threshold, we also assigned detections as certain when surveyors visually observed and recorded colored leg bands on Florida Grasshopper Sparrows that were attached during targeted mist netting captures.
Surveyors recorded date of each point count survey and time-ofday when they initiated each point count.We converted these data to ordinal date of point count (DATE) and hours after civil twilight when a point count began (HOUR).Ordinal date is the number of days after 1 January that a point count was conducted, and hours after civil twilight was the number of hours after civil twilight that a point count was initiated.

Fig. 2. Histogram of nonbreeding eastern Grasshopper
Sparrow (A. s. pratensis) detections that could be misidentified as Florida Grasshopper Sparrow (Ammodramus savannarum floridanus) in Florida using eBird data from 1995-2012.We used these data to determine a threshold (dashed line on 1 May) when we considered Florida Grasshopper Sparrow to be detected with certainty because nonbreeding eastern Grasshopper Sparrows had moved from the area.We excluded data from counties where breeding populations of Florida Grasshopper Sparrow were known to exist.This threshold informed certainty of detections in occupancy models that account for detection (false negative) and misclassification (false positive) probabilities.

Fire variables
We compiled fire data from Avon Park from 1977 to 2011, when adequate spatial fire data existed.These polygon shapefiles varied in spatial resolution.Early fire shapefiles depicted fire at the level of management units, and these data increased in resolution over time to include details of burnt and unburnt areas within management units.We used ArcGIS version 10.6.1 (ESRI, Redlands, CA, USA) to create spatial layers (gridded shapefiles) from prescribed fire polygon shapefiles.We created 5-m grid shapefiles to estimate years-since-fire for each 5-m grid cell each year.We used 5-m resolution to capture fine-scaled details provided in fire data during later years.These shapefiles contained the date of most recent fire for each 5-m grid cell.The spatial scale of fire data is somewhat arbitrary here because we did not attempt to make spatial predictions across the landscape, nor did we use spatially-explicit models.The fine resolution is used here to capture more realism within the fire data.
For each year, we calculated the time interval between the date of most recent fire and the latest date (8 July) of point count surveys over the entire survey period.Hereafter we refer to this time interval as "years-since-fire" (YSF, Fig. 3, Table 1).We summarized years-since-fire as the mean, maximum, and minimum for all 5-m grid cells within two spatial scales that included 100-m and 400-m radius circular buffers around each point count location.The 100-m circular buffer approximated the area of a male Florida Grasshopper Sparrow's territory (Delany et al. 1995, Aldredge 2009).The 400-m buffer approximated the distance between point count stations, which was designed to approximate the maximum distance that a male typically moves when establishing a new territory across years and is an area that can encompass several concurrent territories (Dean et al. 1998).We imputed zero years-since-fire in 1977 for grid cells that burned prior to 1977, and these cells increased by one year-since-fire increments during subsequent years until the grid cells were burned because these cells had not burned for at least that length of time.
We calculated a variable that represented the time of year that the most recent burn occurred in each 5-m pixel and hereafter we refer to this variable as "seasonality" (SEAS, Fig. 4, Table 1).To obtain seasonality, we used standard methods to include circular data as covariates in regressions (Crawley 2007, p. 709-711).We calculated the proportion of a year that lapsed from the ordinal date of the last fire to 1 January during the same year.We converted the proportion of a year to radians by multiplying by 2π where pi refers to the mathematical constant that describes the ratio of a circle's circumference to its diameter.We included seasonality in the model by decomposing seasonality into two components and calculating the cosine and sine of radians where values can range from -1 to 1.The component cosine of SEAS can be interpreted as "winterness" where -1 is summer and 1 is winter.The component sine of SEAS can be interpreted as "springness" where -1 corresponds to fall and 1 corresponds to spring.This variable was included as a covariate to allow dynamics to cycle during the year (described further in Statistical analysis).

Occupancy model
We used hierarchical generalized linear models to specify a dynamic occupancy model that accounted for detection probability (i.e., false negatives, MacKenzie et al. 2002, Tyre et al. 2003) and misclassification (i.e., false positives, Miller et al. 2013) within a Bayesian framework, thereby extending the single-season Table 1.Covariates included in our final analysis using Gibbs variable selection to evaluate the effects from fire on occupancy dynamics of Florida Grasshopper Sparrow (Ammodramus savannarum floridanus) at Avon Park Air Force Range, FL, USA.Seasonality and years-since-fire were summarized at two spatial scales, 100-m and 400-m, and using three functions, the mean, maximum, and minimum values within spatial buffers.site confirmation design (Chambert et al. 2015) to multiple seasons with temporal dynamics (Miller et al. 2013, Louvrier et al. 2019).We used the site confirmation design because it allowed three states of detection to be input into the model including (1) no detection, (2) uncertain (i.e., ambiguous) detection, and (3) certain (unambiguous) detection, and these states were compatible with available data.Organizing the data in this way allowed us to account for detection probability and misclassification while estimating occupancy and dynamics.Our study included data from multiple years, therefore, we used dynamic occupancy models that account for sampling at two temporal scales: 1) a closed period during each breeding season when occupancy was assumed to be stable, and 2) an open period between each year that allowed for changes in occupancy from persistence and colonization (Mackenzie et al. 2006).Florida Grasshopper Sparrows can move among sites within a breeding season (Tucker et al. 2010), and the assumption of closure during each breeding season is likely to be violated; therefore, we interpreted occupancy as the probability of site use during each breeding season.
The first observed state, "no detection," was the outcome when a site was either occupied by the focal species and no individuals were detected, or a site was unoccupied and without misclassification.The second observed state included, "uncertain detections," and was the outcome when a site was occupied and surveyors had an uncertain detection (i.e., there was ambiguity which subspecies was detected), or the site was unoccupied by the focal species but was misclassified as being occupied.We considered uncertain detections to include detections between 1 March and 1 May when eBird data suggested the potential presence of Eastern Grasshopper Sparrows in Florida counties.The third observed state included "certain detections" and was the outcome when a site was occupied by the focal species and a surveyor detected an individual with certainty.We considered certain detections to include banded FGSP that were resighted at any time during the breeding season and any Grasshopper Sparrows detected after 1 May based on eBird data which suggested few Eastern Grasshoppers Sparrows were detected after 1 May.
We added complexity to models using covariates and link functions to customize for the Florida Grasshopper Sparrow.Detection probability included the covariates ordinal date of point count (DATE) and hours after civil twilight when a point count was conducted (HOUR, Table 1 for full descriptions) as quadratic polynomials.We included a random intercept for year.We included both covariates (DATE and HOUR) for detection probability as quadratic polynomials.Probability of misclassification could vary as a function of DATE as a quadratic polynomial and included a random intercept for year.We allowed the probability of certainty to vary with DATE as a cubic polynomial because eBird data indicated that most Eastern Grasshopper Sparrows (> 99%) in the region were detected before 1 May.
We specified initial occupancy state to have a mean intercept without covariates.We included years-since-fire (YSF) and seasonality of the most recent fire (SEAS) and their interactions as covariates for dynamics (i.e., persistence and colonization).Seasonality covariates for persistence and colonization allowed a wave-like response over the duration of a year.This response could have a peak and a trough that were determined by modelestimated parameters.As an example of an effect from seasonality, ordinal date of the most recent fire could influence persistence, and this response would have a peak during times of year when persistence was greatest and a trough when persistence was least.However, the mean response could become a flat line when these coefficients equal zero, indicating no seasonality.We included interaction terms as covariates of both persistence and colonization between YSF and SEAS, YSF 2 (quadratic polynomial) and SEAS, and included random effects for year.All covariates were centered on their mean value and scaled to provide more meaningful interpretation of parameters (Schielzeth 2010) and to ease computation.For additional details of model specifications, refer to Appendix 1.

Covariate reduction and model selection
We implemented covariate reduction and model selection within a Bayesian framework.We reduced the number of covariates using preliminary analyses having two stages of covariate reduction that included an assessment of detection covariates During the first stage using 85% CIs, we processed a detection model that included all a priori covariates for detection, certainty, and misclassification probabilities.We retained these covariates when 85% CIs did not intersect zero.We used 85% CIs threshold because more relaxed thresholds are sometimes used in the context of wildlife management (Miller et al., 2019(Miller et al., , 2016) ) and associations with covariates might change slightly as we built more complex models and account for variation in the data (Appendix 2a).
During the second stage, we used BLISS for additional variable reduction because it can be used to compare correlated covariates (Stuber et al. 2017), such as the minimum, maximum, and mean of years-since-fire that we measured at multiple nested spatial scales.The BLISS method forced the model to choose between correlated covariates so that only one covariate could occur in the model during a single iteration.The covariate that was included most frequently during model iterations was the most likely covariate of those assessed (Stuber et al. 2017).We included yearssince-fire and seasonality as covariates for both persistence and colonization, and we calculated these covariates at two spatial scales using 100-m and 400-m buffers from the point count location.We included year-since-fire covariates as linear and quadratic covariates, and we included the minimum, maximum, and mean YSF calculated using both buffers (Appendix 2b).We retained covariates with the greatest probability of being selected for further analyses using GVS (Appendix 2c).
During the third stage of model selection, we retained the most supported variables from BLISS variable reduction and used GVS to compare model probabilities using evidence ratios.GVS uses a Bernoulli indicator variable to estimate the probability of inclusion for each covariate.During each posterior iteration of the model, this indicator variable can have a value of zero when the model estimates that the covariate should not be included, or the indicator variable can have a value of one when the model estimates that the covariate should be included.Over many posterior iterations, we can obtain the posterior probability for each model and combination of covariates considered here.We used GVS to calculate the probability of each model given the data and the model set.Full implementation of GVS is complex and beyond the scope of this manuscript, and this method is fully described elsewhere (Ntzoufras 2002).
We calculated model-averaged coefficient estimates for persistence and colonization from the subset of posterior distributions when a covariate was included in the model (i.e., when its corresponding Bernoulli indicator variable equaled one).We model-averaged other parameters that did not include a Bernoulli indicator variable by providing estimates from their entire posterior distribution during the model selection process.We assessed the support given to covariates from GVS using an information theoretic framework using evidence ratios and credible intervals (CIs).We used evidence ratios to compare each model to the most supported model having the greatest model probability.Following Burnham and Anderson (2002, p.78) we considered models with evidence ratios between 1.0 and 2.7 to have substantial support; between 2.7 and 33.1 to have weak support; and > 33.1 had no support.We considered covariates to have an association when they received substantial support and 95% CIs did not intersect zero or to have a potential association when 85% CIs did not intersect zero.Arnold (2010) suggested a similar threshold when using model selection with AIC and frequentist confidence intervals, and while not exactly analogous to model selection used here, other studies have similarly used more relaxed confidence intervals when using model selection frameworks (Hein et al. 2008, Long et al. 2008) and when considering wildlife management (Miller et al., 2019(Miller et al., , 2016)).

Model implementation
We performed analyses using R v3.6.1 (R Core Team 2019) and the R package NIMBLE v0.8.0 (NIMBLE Development Team 2019).NIMBLE obtains parameter estimates using Markov Chain Monte-Carlo within a Bayesian framework and we used this software to implement models, covariate reduction, and model selection.Data and code for occupancy models that include detection probability and misclassification are archived online at https://doi.org/10.5281/zenodo.7987218and a detailed workflow can be found in the file docs/index.html.
We used six Markov chains, each having a burn-in of 400,000 iterations and 200,000 iterations for the posterior distribution and thinned one out of every 200 iterations.We visually inspected traceplots of Markov Chain Monte-Carlo to assess convergence for each parameter.We used vague priors for all estimated parameters including uniform (a = 0, b = 1) for intercepts on the probability scale; normal (mean = 0, sd = 100) for coefficients on the logit scale; and half-normal (mean = 0, sd = 10) for sigma parameters of random effects.We assigned prior probabilities for GVS parameters using methods that are fully described elsewhere (Ntzoufras 2002).

RESULTS
We retained 173 point count locations and totaled 7938 point count surveys during 1996-2011.We detected 943 Grasshopper Sparrows, of which 456 were uncertain detections and 487 were certain detections that included detections after 1 May or resightings of color-banded birds.Of these certain detections, only 15 detections included color-banded birds before 1 May.Results from preliminary analyses for covariate reduction using 85% CIs and BLISS are summarized in Appendices 2a and 2c, respectively.

Certainty and misclassification probability from GVS model selection
In final analysis using GVS, the probability of misclassification had a quadratic relationship with date of survey (DATE 2 , Table 2), increasing through late March, peaking in mid-April with an average probability of 0.05 across all years, and decreasing through late April and early May to near zero (Fig. 5).When averaged across the entire breeding season, the probability of misclassification was relatively low (0.00-0.01); however, misclassification probabilities were much greater (0.01-0.27) during seasonal peaks (12 April, Figs. 5 and 6).Certainty had an association with cubic polynomial of date of survey (i.e., DATE 3 , Table 2).Certainty was near zero during March, increased slightly in early April, then decreased to near zero until late April and early May when certainty increased to near perfect (1.0) for the remainder of the season (Fig. 5), coinciding with the threshold of 1 May when detections of unbanded birds were assigned to be certain.Certainty had a cubic response, and misclassification had a quadratic response to ordinal date.Solid lines depict modeled means and gray polygons depict 95% credible intervals.The dashed vertical line depicts the cutoff date after when eBird data suggested that eastern Grasshopper Sparrows (A. s. pratensis) that can be misidentified as Florida Grasshopper Sparrows were unlikely.

Habitat use and dynamics: persistence and colonization from GVS model
Overall, the probability of persistence by Florida Grasshopper Sparrows decreased when patches were left unburned for long periods and fluctuated with seasonality of last burn.The probability of persistence was associated with maximum yearssince-fire within a 400-m buffer (YSF, Fig. 7), seasonality within a 100-m buffer (sinSEAS, Fig. 7), and a random effect for year (YEAR, Fig. 6).This model had substantial support (evidence ratio = 1.0,Table 3), and 95% CIs for coefficients did not intersect zero (Table 2), indicating additional support.The average probability of persistence was associated with seasonality and persistence was greatest (0.97, Fig. 7) when all pixels within a 400m buffer of the point count location were recently burned near 3 April (YSF < 1) and was least (0.03) when any pixel did not burn for 35 years near 1 October.The probability of persistence was greater than average between January and July; peaked on 3 April; and was lower than average between July and January with a nadir on 1 October.However, two models that excluded seasonality (both sinSEAS and cosSEAS) received substantial support (evidence ratios of 1.0 and 2.5, respectively), indicating some uncertainty regarding model selection for this covariate.The probability of colonization by Florida Grasshopper Sparrows was low overall (< 0.05) and peaked approximately two months after fire (Fig. 8).The probability of colonization was correlated with minimum years-since-fire squared within a 400-m buffer (YSF 2 ).The model including this covariate had substantial support (evidence ratio = 2.5), and 85% CIs (-11.54--0.67)did not intersect zero indicating a potential association.Models including seasonality within 100-m buffer (i.e., sinSEAS) as a covariate for the probability of colonization had only weak support (evidence ratio ≥3.8), but 95% CIs of seasonality (sinSEAS) did not intersect zero adding some support for this covariate having an association.The probability of colonization by Florida Grasshopper Sparrows varied by year and models including the random effect for year had substantial support (e.g., evidence ratio of ≥1.0, Table 3).

DISCUSSION
To enable more accurate and precise estimates of habitat use for a critically Endangered bird, the Florida Grasshopper Sparrow, we used dynamic occupancy models to investigate the role of prescribed fire on aspects of habitat use, while also accounting for the presence of eastern Grasshopper Sparrows.Determining accurate habitat use for an endangered species is vital to monitoring and conservation efforts.Modeling both false Table 3. Model probabilities estimated from Gibbs variable selection for occupancy dynamics of Florida Grasshopper Sparrow (Ammodramus savannarum floridanus) including persistence (ϕ) and colonization (γ) from occupancy models that account for detection and misclassifications.Covariate abbreviations for persistence include maximum years-since-fire within a 400-m buffer (YSF), seasonality of last burn within a 100-m buffer (SEAS), and a random effect for year (YEAR).Covariate abbreviations for colonization include minimum years-since-fire squared using a 400-m buffer (YSF2) seasonality of last burn using a 100-m buffer (SEAS) and a random effect for year (YEAR).Seasonality covariates are either sine-transformed (sinSEAS) or cosine-transformed (cosSEAS).We considered models to have substantial support when evidence ratios were between 1.0 and 2.7; weak support when between 2.7 and 33.1; and no support when > 33.1 (Burnham and Anderson 2002).Interactions are depicted with a colon (:).negatives and misclassification (false positives) allowed us to determine a probability for detections that reduced biases caused by sympatry with a similar subspecies at the time of surveys for the Florida Grasshopper Sparrow (Royle and Link 2006).
Fire maintains the Florida dry prairie in an early successional stage and prevents encroachment of trees and tall shrubs (Platt et al. 2006).Prior studies show that Florida Grasshopper Sparrows prefer recently burned dry prairie and occasionallygrazed pasture (Delany et al. 1985, Walsh et al. 1995, Hewett Ragheb et al. 2019).We found that the probability of persistence was greatest in recently burned habitat (<1 years-since-fire), comporting with previous research (Walsh et al. 1995).The probability of colonization was also highest for recently burned habitat at the 400-m spatial scale but for the minimum year-sincefire variable.These results suggests that frequent fires within a larger spatial scale (400-m) are beneficial for retaining and attracting Florida Grasshopper Sparrows.Delany et al. (1995) found that marked Florida Grasshopper Sparrows tended to stay in the same breeding territory for 2-4 successive years.The maximum years-since-fire was 35 years over the time period we sampled, which implies that at least part of the 400-m radius buffer circle included areas that did not regularly burn, such as depression marshes, cypress domes, or military infrastructure.Between 1996 and 2009, the mean fire return interval in dry prairie at Avon Park was 2.3 years (Rolek et al. 2009), with some areas burned more frequently due to military exercises but other areas burned less frequently (> 3 years).Between 2001 and 2003, a period of steep decline in the Florida Grasshopper Sparrow population, the fire return interval averaged 3.3 years.Our result confirms that Florida Grasshopper Sparrows persist in extensive areas (at least 400 m in radius) that were recently and frequently burned.
The presence of false positives in data can lead to biased occupancy estimates but can be corrected by determining the misclassification probability (Miller et al. 2013, Ruiz-Gutierrez et al. 2016, Berigan et al. 2019).We found a peak in the probability of misclassification (0.271) and a low probability of certainty (0.0) in April, which corresponds to an increase in migratory movement of eastern Grasshopper Sparrows in Florida (Vickery 1996).Misclassification probability decreases and certainty increases by May, after most eastern Grasshopper Sparrows have left Florida, however, some may begin singing on their wintering grounds prior to migration.Point count surveys for the Florida Grasshopper Sparrow generally start in late March or early April, at the start of their breeding season, thus in some years there may be as much as a month when males of both subspecies are singing.Point count surveys conducted after eastern Grasshopper Sparrows leave in May have a higher certainty of detection but also may be less likely to detect Florida Grasshopper Sparrows given lower levels of nesting synchrony and singing at that point in the breeding season (Delany et al. 2013, Lohr et al. 2013).Explicitly modeling certainty of detections and misclassifications allows for surveys to be completed at the most likely time to detect Florida Grasshopper Sparrow while also accounting for the presence of the eastern Grasshopper Sparrow.
The influence of fire seasonality on Florida Grasshopper Sparrow nesting and territory density has been the focus of many studies attempting to determine the most effective burning season for management that optimizes survival and reproduction (Shriver et al. 1996, Shriver and Vickery 2001, Hewett Ragheb et al. 2019).
Fire seasonality can influence floristic composition (Waldrop et al. 1992), which in turn can impact vegetation cover for nesting and survival (Larned et al. 2020).Our results suggest that at the territory scale (100-m buffer), Florida Grasshopper Sparrows are more likely to persist between years when a fire occurred between January and July, with a peak in early April.There was weak support between fire seasonality and colonization with a peak corresponding to fires burned in October for Avon Park, which could be attributable to the overall decline in colonizations over time.
Prescribed fire management, and its timing, is an important tool currently used for maintaining habitat for the Florida Grasshopper Sparrow (Hewett Ragheb et al. 2019).Our results show fire influenced persistence and colonization differently, which means that practitioners could vary timing of fire to optimize demographic rates; and patches within a site could be managed depending on the current occupancy status.For example, if the management goal is to retain Florida Grasshopper Sparrows in a patch or attract them to an unoccupied patch, then the timing of fire would be applied so that persistence and colonization are optimized for specific circumstances of a habitat patch.Thus, management of Florida Grasshopper Sparrow habitat can be administered within patches to achieve specific occupancy goals for maintaining populations in an area.

CONCLUSION
Our results clarify that the number of sites used by Florida Grasshopper Sparrows at Avon Park declined from 111 to 25 during 1996 to 2003 and fluctuated between 10-23 occupied sites during 2004-2011, reaching a nadir of 2 in 2012.Recent results using uncorrected count data suggest a slight increase of singing males from 2 in 2012 to 6 in 2019 (Bowman, unpublished data).Furthermore, our results provide inference about responses by Florida Grasshopper Sparrows to prescribed fire in greater detail than has previously been described.
Decreasing bias in occupancy models is vital for accurately estimating the population dynamics of endangered species for the purposes of determining their status and improving monitoring efforts (McClintock et al. 2010, Miller et al. 2015).We used models that account for misclassification to reduce biases and improve habitat use estimates to determine the influence of prescribed fire management on Florida Grasshopper Sparrows.These models provide a flexible and extensible method for future studies where misclassifications may be problematic.Many scenarios exist where our approach may be useful when species or subspecies are challenging to differentiate during surveys.We combined semistructured data (e.g., Ebird) with dynamic occupancy models that account for misclassifications to leverage differences between subspecies by their spatial and temporal distributions, thereby providing a novel solution that may clarify population trends, habitat associations, and responses to management of other wildlife when they are potentially misclassified.We specified initial occupancy state as ( ,=1 ) =  ,=1 .We included years-since-fire (YSF) and seasonality of the most recent fire (SEAS) and their interactions as covariates for dynamics (i.e., persistence and colonization).Seasonality covariates for persistence and colonization allowed a wave-like response over the duration of a year.This response could have a peak and a trough that were determined by model-estimated parameters.As an example of an effect from seasonality, ordinal date of the most recent fire could influence persistence, and this response would have a peak during times of year when persistence was greatest, and a trough when persistence was least.However, the mean response could become a flat line when these coefficients equal zero indicating no seasonality.We included interaction terms as covariates of both persistence and colonization between YSF and SEAS, YSF 2 and SEAS, and included random effects for year (  ,   ).

Fig. 1 .
Fig. 1.Map of point count locations at Avon Park Air Force Range, Polk and Highland Counties, FL, USA.The shaded grey areas are historic dry prairie habitat.The excluded point counts refer to survey points where Florida Grasshopper Sparrows (Ammodramus savannarum floridanus) were not detected during the study period.

Fig. 3 .
Fig. 3. Years-since-fire (YSF) near 173 point count locations within Avon Park Air Force Range, FL, USA during 1977 through 2011.Colors depict the number of 5-m grid cells that burned each year.Years-since-fire is depicted for 100-m spatial buffers (left) and 400-m spatial buffers (right) from the center of point count locations.Dashed vertical lines depict the initiation of point count surveys in 1996.We inputed zero years-since-fire in 1977 for grid cells that burned prior to 1977, and these cells increased by one year-since-fire during subsequent years until a grid cell was burned.Inputed cells were known to have not burned for at least that length of time.

Fig. 4 .
Fig. 4. Seasonality (SEAS) of most recent fires at grid cells near 173 point count locations within Avon Park Air Force Range, FL, USA during 1977 through 2011.Colors depict the number of 5-m grid cells having most recent fire during categorized seasons.Seasonality was a continuous variable that we categorized as quarters (top) and growing seasons (bottom) for each year to aid with visualization.Seasonality is summarized within 100-m spatial buffers (left) and 400-m spatial buffers (right) from the center of point count locations.Dashed vertical lines depict initiation of point count surveys in 1996 that were included in our study.Naturally occurring fire seasons are dormant (Oct-Mar), transition (Apr-Jun), and growing (Jul-Sep) seasons.

Fig. 5 .
Fig. 5. Probability of misclassification and certainty of detections for Florida Grasshopper Sparrow (Ammodramus savannarum floridanus) in response to DATE (days after 1 March) during the breeding season.We obtained estimates from a dynamic occupancy model that accounted for detection probability and misclassification applied to point count data at Avon Park Air Force Range, Florida, USA during 1996-2011.Certainty had a cubic response, and misclassification had a quadratic response to ordinal date.Solid lines depict modeled means and gray polygons depict 95% credible intervals.The dashed vertical line depicts the cutoff date after when eBird data suggested that eastern Grasshopper Sparrows (A. s. pratensis) that can be misidentified as Florida Grasshopper Sparrows were unlikely.

Fig. 6 .
Fig. 6.Probabilities of detection, certainty, misclassification, occupancy, persistence, and colonization of Florida Grasshopper Sparrows (Ammodramus savannarum floridanus) each year during 1996-2011 from a dynamic occupancy model that accounted for detection probability and misclassification.This model was applied to point count data during the breeding season at Avon Park Air Force Range, FL, USA.Lines depict average estimates and gray polygons depict 95% credible intervals.

Fig. 7 .
Fig. 7. Probability of site persistence of Florida Grasshopper Sparrow (Ammodramus savannarum floridanus) in response to years-since-fire and seasonality of last fire.We obtained estimates from a dynamic occupancy model that accounted for detection probability and misclassification.We applied this model to point count data collected during 1996-2011 at Avon Park Air Force Range, FL, USA.Solid lines depict modeled averages and gray polygons depict 95% credible intervals.The top two panels depict isolated effects while other covariates are held at their mean values.The bottom panel depicts combined effects of seasonality and years-since-fire.

Fig. 8 .
Fig. 8. Probability of site colonization of Florida GrasshopperSparrow (Ammodramus savannarum floridanus) in response to years-since-fire (400 m buffer) and seasonality of last fire (100 m buffer).Solid lines depict modeled means and gray polygons depict 95% credible intervals.We obtained estimates from a dynamic occupancy model that accounted for detection probability and misclassification.We applied this model to point count data collected during 1996-2011 at Avon Park Air Force Range, FL, USA.The model that included minimum years-since-fire within a 400-m buffer (upper panel) had substantial support, while models that included seasonality of burn within 100-m buffer (lower panel) had weak support.

Table 2 .
Parameter estimates from dynamic occupancy models and Gibbs variable selection that account for misclassification and detection probability applied to point count survey data from 1996-2011 at Avon Park Air Force Range, FL, USA.Estimates for the probabilities of persistence and colonization are averaged over models when Bernoulli indicator variables equal one, while other estimates are averaged over all models.
A. F. L. and B. W. R. conceived the study, wrote the manuscript, and contributed equally to this work as co-lead authors.B. W. R.
developed the models; K. S. contributed to GIS data analyses; S. P. contributed to early versions of data analyses; R. B. conceived the study and supervised the field research; and B. L. edited the manuscript.