Abstract
Quantifying habitat occupancy of the southeastern beach mouse Peromyscus polionotus niveiventris is important for managing this threatened species throughout its limited range. Tracking tubes were used to detect the southeastern beach mouse in coastal areas on the federal lands of the Kennedy Space Center, Cape Canaveral Air Force Station, and Canaveral National Seashore. Because this method relied on observations of footprints, detections of beach mice were confounded by the co-occurrence of cotton mice Peromyscus gossypinus, which have wider but slightly overlapping footprint widths. Mice of both species were captured and footprinted using tracking tubes to collect a database of footprints of known identity. These data were used to develop a Bayesian hierarchical model of the cutoff width at which a print could be assigned as a beach mouse with a known probability of error. Specifically, within the model, observed footprint widths were used to estimate a mean and variance of footprint width for each species, while accounting for variation between individual mice. Then, a distribution of new footprint widths was generated for each species by drawing from their modeled distributions. Finally, the new footprints were compared with a range of potential cutoff widths to evaluate the proportion of times the correct decision to exclude or accept the footprint was made. We graphically evaluated the performance of the cutoff widths and chose one that traded off between reducing false positives and retaining more correct detections for use in occupancy models. We explored the use of the cutoff width using occupancy models that allow for false-positive detections, and found that the use of the cutoff performed as expected. Over 40% of primary dune habitat on the Kennedy Space Center was occupied by beach mice during the period sampled. The proportion of vegetated habitat at a site had a negative influence on detection probability. No ecological covariates had a measurable influence on beach mouse occupancy, probably due to the limited range of environmental variation in the sampled region. The use of a cutoff for footprint width resulted in a reliable method to deal with false-positive detections in tracking tubes with small mammals and allowed the use of occupancy models that rely on certain detection.
Introduction
The southeastern beach mouse Peromyscus polionotus niveiventris (Figure 1) is one of seven extant isolated subspecies of the old field mouse P. polionotus known as beach mice that inhabit barrier islands of Alabama and Florida (Hall 1981). Habitat loss from coastal development and other anthropogenic activities has reduced the abundance and range of beach mice populations and the subspecies is listed as threatened under the U.S. Endangered Species Act (ESA 1973, as amended). One example of this is evident along the Atlantic coast of Florida where the historical range of the southeastern beach mouse formerly extended along approximately 350 km of coastal dunes, from Daytona Beach to Miami Beach (Figure 2; Stout 1992). Today their distribution is restricted to approximately 150 km from Volusia through Indian River counties (Stout 1992; Kalkvik et al. 2012). Within this range the majority of the remaining population occurs along 72 km of coast on the federal lands of the Kennedy Space Center (KSC), Cape Canaveral Air Force Station, and Canaveral National Seashore (hereafter referred to as federal lands surrounding KSC). Species-habitat studies of beach mice on these lands have been conducted over the last four decades with the goal of understanding habitat requirements to guide management (Ehrhart 1976; Stout 1979, Oddy 2000; Stout et al. 2004); most of this work has focused on measuring demographic rates on a limited number of small, isolated sites. There is a need to monitor the subspecies throughout its remaining range to inform managers of its status and habitat requirements.
Tracking tubes (A) were used to detect southeastern beach mice Peromyscus polionotus niveiventris (B) by recording their footprints on federal lands of the Kennedy Space Center, Cape Canaveral Air Force Station, and Canaveral National Seashore, Florida, in December 2009. Similar tubes were used to obtain footprints from captured beach mice (C) and cotton mice Peromyscus gossypinus (not shown) during May 2008–February 2011 for use in developing a model of footprint widths to use in identifying unknown footprints.
Tracking tubes (A) were used to detect southeastern beach mice Peromyscus polionotus niveiventris (B) by recording their footprints on federal lands of the Kennedy Space Center, Cape Canaveral Air Force Station, and Canaveral National Seashore, Florida, in December 2009. Similar tubes were used to obtain footprints from captured beach mice (C) and cotton mice Peromyscus gossypinus (not shown) during May 2008–February 2011 for use in developing a model of footprint widths to use in identifying unknown footprints.
The historic range of the southeastern beach mouse Peromyscus polionotus niveiventris consisted of approximately 360 km of coastal dune habitat from Ponce Inlet (Volusia County) south to Hollywood (Broward County), Florida. The current range has been restricted mainly to the federal lands of the Kennedy Space Center (KSC), Cape Canaveral Air Force Station (CCAFS), and Canaveral National Seashore (CNS). Relict populations are also known to exist at Smyrna Dunes Park (Volusia County), Sebastian Inlet State Park (Brevard County), and Pelican Island National Wildlife Refuge (Indian River County).
The historic range of the southeastern beach mouse Peromyscus polionotus niveiventris consisted of approximately 360 km of coastal dune habitat from Ponce Inlet (Volusia County) south to Hollywood (Broward County), Florida. The current range has been restricted mainly to the federal lands of the Kennedy Space Center (KSC), Cape Canaveral Air Force Station (CCAFS), and Canaveral National Seashore (CNS). Relict populations are also known to exist at Smyrna Dunes Park (Volusia County), Sebastian Inlet State Park (Brevard County), and Pelican Island National Wildlife Refuge (Indian River County).
Tracking tubes are used to detect small mammals without capturing them (Figure 1; Mabee 1998; Loggins et al. 2010). Baited tracking tubes placed within habitat attract small mammals that leave their footprints as evidence of occurrence. To effectively use tracking tubes to estimate habitat occupancy of small mammals, it is necessary to correctly identify the species detected, a task made potentially difficult when other sympatric species have similar footprints (van Apeldoorn et al. 1993). Within areas that provide habitat on the federal lands surrounding KSC there are four sympatric species of small mammal with footprints similar in width to the beach mouse, including cotton mouse, Peromyscus gossypinus; golden mouse, Ochrotomys nuttalli; Florida mouse, Podomys floridanus; and cotton rat, Sigmodon hispidus (D.M.O., personal observation). However, along areas of coastal strand within 0.5 km of the Atlantic Ocean, over 23 y of small mammal trapping studies have captured almost exclusively beach mice and cotton mice (D.M.O., personal observation), thus making the problem of discrimination easier in these areas. Preliminary evidence suggested that the width of beach mouse footprints was generally less than that of cotton mice, although there is uncertainty in discriminating footprints within the region of footprint width overlap.
Habitat occupancy modeling (MacKenzie et al. 2002) is a powerful method often used to identify relationships between a species' habitat use and ecological features that vary across the landscape within its range. Measuring occupancy requires less effort than measuring abundance or demography, thus allowing a broader geographic area to be sampled with a fixed amount of effort. One of the strengths of habitat occupancy modeling is its flexibility in how the target species is detected. Although there have been many refinements to habitat occupancy since its initial formulation, most applications rely on the assumption of no false detections. Royle and Link (2006) explored the effect of violations of this assumption, found that severe bias may occur with even moderate levels of false positives, and developed an extension of the MacKenzie et al. (2002) occupancy model that allows for false positives. Miller et al. (2011) extended the Royle and Link (2006) model to incorporate information about the false-positive detection process; notably, this model allows for both certain and uncertain classes of detections. Uncertain detections might occur when more than one species occurred with similar detection signs, and certain detections might occur if some signs were unique to one of the species. Several recent investigations have highlighted the importance of accounting for false-positive detections in occupancy studies (Fitzpatrick et al. 2009; McClintock et al. 2010). These studies demonstrated that substantial bias can occur in estimates of occupancy when false detections occur and are not accounted for.
To access the utility of tracking tubes as a tool for beach mouse habitat occupancy, we conducted a pilot study in coastal strand within 100 m of the Atlantic Ocean. We also live-trapped small mammals within this habitat and measured their footprints. On the basis of previous knowledge of their relative footprint widths, we reasoned that there would be partial overlap between beach mouse and cotton mouse front footprint widths. Further, we reasoned that we could determine a footprint width cutoff that would adequately discriminate between species to allow habitat occupancy modeling of beach mice without significant bias. The first objective of this study was to quantify a precise footprint width cutoff that would allow a known proportion of all cotton mouse footprints to be correctly identified, thus limiting the problem of false positives of beach mouse to a fixed level. A second objective was to explore the use of information regarding the overlap of footprint widths in occupancy models allowing for both certain and uncertain detections (Miller et al. 2011).
Methods
Known footprint sampling
Footprints were collected May 2008–February 2011 at 97 sampling points in coastal habitat on the federal lands surrounding KSC (Figure 2). Sampling points were either within long-term demographic study grids, or on long-term occupancy survey sample points. Footprint sampling points consisted of two Sherman live traps placed approximately 15 m apart in beach mouse habitat. Most sample points were located within 50 m of the primary dune; however, five sample points were located in scrub approximately 6 km from the primary dune. Trapping efforts followed standard protocols (Oddy 2000) and were operated for one or two nights. To obtain footprints, a blank piece of card stock paper was inserted into a Tyvek sleeve (of the type used to protect credit card magnetic strips) with an ink pad attached that was then placed at the back end of either a clear plastic or polyvinyl chloride tube with an end cap. The animals were inserted into the open end where they proceeded down the tube to the ink pad that inked their feet. Once the animal left a legible print on the paper it was released from the tube at the point of capture. All cards were secured so as to not smear the footprints on the card, and all complete footprints were measured from the outside of the two outer toes of the front foot to the nearest 0.1 mm using calipers. For most mice included in the study, several footprints were measured for two reasons. First, when an animal is footprinted, often several measureable prints occur, so up to five of these were measured. Second, animals were occasionally recaptured during the study, and footprints were recorded during each recapture when possible. All protocols for handling live animals followed American Society of Mammalogists guidelines (Sikes et al. 2011), were approved by an institutional animal care and use committee, and were conducted under U.S. Fish and Wildlife Service federal permit number TE089075-3.
Footprint Bayesian analysis
Our task was to choose a reliable footprint cutoff width below which we could consider a footprint to indicate a beach mouse detection. In addition, we wished to consider the trade-off between minimizing false detections (cotton mice footprints being scored as beach mice) while maximizing valid detections of beach mice. Assuming that within a species the footprint widths are distributed according to some probability distribution with parameters estimated from relevant data, one could pick various cutoff values at which it would be expected that a given proportion of individuals of each species would fall. Therefore, given an adequate sample of footprints of each species, one could determine a footprint cutoff width that would produce the specified level of false detection and true detection rates. We developed a general framework for footprint cutoff analysis and implemented the approach in a Bayesian framework that allowed for direct statements about the probability of events such as footprint misspecification (Link and Barker 2010).
We used WinBUGS version 1.4.3 (Lunn et al. 2000) to analyze the data, implemented in R version 3.0.2 (R Development Core Team 2013) using package R2WinBUGS (Sturtz et al. 2005). The likelihood of the data (footprint widths) was assumed to come from a normal distribution. Because we had multiple measurements of footprints from each individual, we included individuals as a random effect in the analysis; this accounted for the effect of measurement error by increasing the uncertainty in the estimates of mean footprint width for each individual. This was modeled by allowing each individual to be sampled from a normal distribution using an individual-specific standard deviation that was drawn from another normal distribution (Kery 2010). We used uninformative prior distributions for all unknown parameters in the model. For the prior distributions of mean footprint width for each species we used a normal distribution with mean = 0 and variance = 1,000. For both the prior distributions of the standard deviation of mean footprint width for each species and the prior distribution of the standard deviation of the individual group mean within each species, we used uniform distributions on (0, 1). Code to implement the model in R is given in Text S1. WinBUGS was used to generate 100,000 samples from the posterior distribution after discarding the initial 50,000 iterations as a burn-in.
To use information about footprint widths to determine a print cutoff width, we generated predictions of a hypothetical new mouse footprint of each species during each iteration of the Bayesian simulation. On the basis of the assumptions of the statistical distributions used in the model, this distribution characterizes a hypothetical population of mice from which we could potentially draw samples in the future. We used an indicator variable to obtain a distribution of the proportion of simulations resulting in a correct decision to include or reject the new footprints for each potential cutoff width within 6.0–7.5 mm (in 0.1-mm increments). Specifically, within each iteration of the Bayesian Markov chain Monte Carlo sampling, we drew a random footprint from the distributions estimated for each species. Then, for each of these new prints we recorded whether or not the print was classified correctly as a detection for each potential cutoff width for each species. This resulted in a vector of length 150,000 with value of 1 or 0, which represented correct and incorrect classifications respectively. The proportion of correct and incorrect classifications could then be determined for each cutoff value for each species. We plotted these proportions to graphically explore the trade-off resulting from each potential print cutoff width. Our approach is similar to a power analysis that attempts to quantify the trade-off between two related error rates: an error of falsely classifying a nondetection as a detection (type I error rate, i.e., the rate of erroneously rejecting the null hypothesis of a given print being a nondetection), and an error of falsely classifying a detection as a nondetection (type II error rate, i.e., the rate of failing to reject the null hypothesis of a given print being a nondetection). Although it was not clear to us how to calculate this using traditional frequentist procedures, the Bayesian model provided such a method. All parameter estimates were calculated from their posterior distributions, with mean and 95% credible intervals reported.
Occupancy survey
The occupancy study was conducted along 10 km of primary dune on KSC. One-hundred sites were sampled with five tracking tubes at each site with a central tube surrounded by four tubes at the cardinal directions spaced approximately 3 m from the central tube. The central tube was placed approximately 6 m from the dune vegetation/open beach edge. Stations were located by first randomly locating a starting point at the north end of the area to be sampled, then placing the sites approximately 100 m apart using a geographical information system (GIS) to generate the coordinates. Sampling locations were located in the field using a handheld global positioning system (GPS). The tubes were deployed on the morning of December 9, 2009 and retrieved three nights later on the morning of December 12, 2009. During retrieval, GPS positions were recorded for the central tube at each site, and tracking-tube papers were removed and labeled with the date, site number, and tube location.
Tracking-tube creation, assembly, and deployment followed Loggins et al. (2010). Tubes were baited with 5–10 sunflower seeds placed at the closed end of the tube. Tracking papers were cut from cardstock paper to fit into tubes. The ink pad was made from a small felt pad glued to contact paper that was wrapped around a Tyvek sleeve (to prevent the ink mixture from bleeding through). The felt pad was inked with a mixture of carbon lampblack ink suspended in food-grade mineral oil, and the tracking paper was inserted into the end of the Tyvek sleeve and then slid into the tube with the inked end at the tube entrance (90° elbow joint). Papers were bent into a slightly convex shape before insertion so that they would conform to the bottom surface of the tube. This helped to prevent mice from crawling under the paper and thereby missing the ink pad and paper surface. Further details of tracking-tube and paper design can be found in Loggins et al. (2010). In the lab, three independent observers measured the width of the smallest mouse footprints on each tracking tube paper. When using a cutoff footprint width to determine evidence of beach mouse detection, agreement of two of the three observers determined the outcome.
Occupancy models
We explored two strategies to assess possible misidentification of beach mice in our occupancy survey. The first approach was based on a cutoff width above which any prints would not be considered as a detection, because we reasoned that the wider prints were more likely to be cotton mice. We used information from the Bayesian analysis of footprint widths to determine the cutoff value that optimized the exclusion of false positives and the inclusion of correct detections. To assess the utility of using the footprint cutoff we fit the model presented in Royle and Link (2006) that includes a false-detection parameter, and compared that with the Mackenzie et al. (2002) occupancy model that assumes no false detections. The second approach used all observed footprints in an analysis, allowing some detections to be certain and others to be subject to uncertainty (Miller et al. 2011). We used the observed footprint widths to assign observations to a class of certain detections (footprints small enough to be almost certainly of beach mice) and uncertain detections (those between the certain detection width and the maximum cutoff width). We fit all models to our beach mouse occupancy data in R (R Core Development Team 2013) using the unmarked package (Fiske and Chandler 2011) and used model selection based on Akaike information criterion (AIC) to rank relative support for models within each occupancy model type. Model averaging was conducted using package AICcmodavg (Mazerolle 2013). For the MacKenzie et al. (2002) model and the Royle and Link (2006) model, we used 7.2 mm as the cutoff below which we considered a footprint to indicate a beach mouse detection. For the Miller et al. (2011) model, the width at which we considered a detection to be certain was below 6.1 mm, with footprints 6.1–7.1 mm considered to be subject to misspecification. Justification of these values resulted from the Bayesian model of footprint widths (see below).
For all three types of occupancy models, we investigated a limited set of models allowing covariates on the detection and occupancy parameters. These covariates were chosen on the basis of the hypothesis that beach mice occupied specific patches of habitat that are frequently disturbed by events such as storms, predation, or fire that cause local extirpation followed by recolonization of sites. Although we were measuring static occupancy during a closed period, we believed that landscape features might determine occupancy by serving as dispersal barriers, thus causing more isolated sites to have lower occupancy rates. Covariates were measured from existing land use and land cover classification maps (R. Schaub, unpublished map) and color aerial photography (obtained October 29, 2008) using a GIS. Four site covariates were considered for the occupancy parameters: 1) 10mpVeg, the proportion of unvegetated habitat within 10 m of the center position of each site, because beach mice may prefer more or less vegetated habitat; 2) roadRR, the distance to the nearest hard infrastructure (e.g., train track or paved road), which may serve as a barrier to dispersal, thus affecting recolonization after local extripation; 3) scrub, the distance to the nearest oak scrub habitat, which may be a habitat from which the beach is recolonized after extirpation due to disturbance such as hurricanes (Oddy 2000; Stout et al. 2004, 2007); and 4) duneW, the width of beach dune habitat at the sample point, which was thought to be a general indicator of amount of habitat and connectivity with other sites. The proportion of unvegetated habitat within 10 m of the center position of each site (10mPVeg) was also considered as a covariate on the detection parameter, since more exposed sites may have higher predation risk, which could affect beach mouse foraging behavior. We fit separate models with each of the covariates (or none) on the occupancy parameter, with or without the covariate on the detection parameter, for a total of 10 models. We did not consider any covariates for the probability of false detection or the probability of certain detection for the Royle and Link (2006) or Miller et al. (2011) models.
Results
Footprints
Two-hundred-twenty-five small mammals were captured and footprinted during the study, including 56 cotton mice, 134 beach mice, 2 golden mice, 1 Florida mouse, and 32 cotton rats. Of the cotton mice, 47 were captured once, 8 were captured twice, and 1 was captured three times. Of the beach mice, 112 were captured once, 18 were captured twice, 3 were captured three times, and 1 was captured four times. As expected, the distribution of footprint widths appeared to be normally distributed for each species, justifying the use of this distribution in the Bayesian statistical model (Figure 3). Footprint data are included in Text S2. The Bayesian model of mouse footprint widths showed good mixing within the chains with no significant autocorrelation in the samples after burn-in. The mean of the posterior distribution of footprint widths and the variance between and within individuals of each species are given in Table 1. There was a similar degree of variation within individuals as between, as can be seen by comparing the standard deviation for the between-individual variation (sigma residual) with that for individuals (sigma individual). The footprint width that maximized retention of beach mouse detections while minimizing false detections due to cotton mice was between 7.2 and 7.3 mm (Figure 4). On the basis of these results, we considered mouse prints less than 7.2 mm in width as potential beach mouse detections for the Mackenzie et al. (2002) and the Royle and Link (2006) models. This choice balanced the competing requirements in an optimal manner, although other choices of how to achieve this balance might also be reasonable. Specifically, this choice maximized both the probability of excluding a cotton mouse print and the probability of retaining a beach mouse print. Given that our precision to measure prints was limited to 0.1 mm, we included prints 7.1 mm and smaller to capture the optimal within our ability to measure. From the Bayesian model results, a footprint of 6.1 mm had a probability of belonging to a cotton mouse < 0.04 (Figure 4). Thus, for use in the Miller et al. (2011) model we chose to consider prints of width 6.0 or less as certain beach mouse detections and widths 6.1–7.1 as uncertain detections; prints 7.2 and above were considered nondetections.
Observed distribution of footprint widths of beach mice Peromyscus polionotus niveiventris and cotton mice Peromyscus gossypinus captured on federal lands of the Kennedy Space Center, Cape Canaveral Air Force Station, and Canaveral National Seashore, Florida, May 2008–February 2011. Footprint widths overlap extensively in the region 7–8 mm. The figure shows the distribution for all measured footprints including repeated measurements within the same individuals.
Observed distribution of footprint widths of beach mice Peromyscus polionotus niveiventris and cotton mice Peromyscus gossypinus captured on federal lands of the Kennedy Space Center, Cape Canaveral Air Force Station, and Canaveral National Seashore, Florida, May 2008–February 2011. Footprint widths overlap extensively in the region 7–8 mm. The figure shows the distribution for all measured footprints including repeated measurements within the same individuals.
Trade-off between eliminating false detections (designating a cotton mouse Peromyscus gossypinus print as a detection) and retaining true detections. For each cutoff value, the plot shows the probability that a cotton mouse print is excluded and the probability that a beach mouse print Peromyscus polionotus niveiventris is included. Values are based on the results of the Bayesian model of footprints for mice on federal lands of the Kennedy Space Center, Cape Canaveral Air Force Station, and Canaveral National Seashore, Florida. The horizontal lines indicate the regions in which prints were excluded as probable false detections (above 7.1 mm), the region in which detections were considered uncertain (6.3–7.1 mm), and the region in which prints were considered to be certain detections (below 6.2).
Trade-off between eliminating false detections (designating a cotton mouse Peromyscus gossypinus print as a detection) and retaining true detections. For each cutoff value, the plot shows the probability that a cotton mouse print is excluded and the probability that a beach mouse print Peromyscus polionotus niveiventris is included. Values are based on the results of the Bayesian model of footprints for mice on federal lands of the Kennedy Space Center, Cape Canaveral Air Force Station, and Canaveral National Seashore, Florida. The horizontal lines indicate the regions in which prints were excluded as probable false detections (above 7.1 mm), the region in which detections were considered uncertain (6.3–7.1 mm), and the region in which prints were considered to be certain detections (below 6.2).
Parameter estimates from the results of a Bayesian model of footprint width for beach mice Peromyscus polionotus niveiventris and cotton mice Peromyscus gossypinus on federal lands of the Kennedy Space Center, Cape Canaveral Air Force Station, and Canaveral National Seashore, Florida, May 2008–February 2011. Table entries are given for each species for the estimated mean footprint width (μPg, μPp), random-effect standard deviation (σind.Pg, σind.Pp), residual standard deviation (σres.Pg, σres.Pp), and the predicted standard deviation (σnew.Pg, σnew.Pp) and mean (μnew.Pg, μnew.Pp) for a hypothetical new individual. Columns give the mean, standard deviation (SD), credible interval end points (2.5%, 97.5%), median (50%), and diagnostics (Rhat and n.eff) for the posterior distributions from the Bayesian analysis.

Occupancy models
The models with no covariate on the occupancy parameter and 10mpVeg (the proportion vegetated within 10 m of the site center) on the detection parameter had the highest support among alternative models for all three types of occupancy model (Table 2). The models that added each of the additional covariates on the occupancy parameter also had some support for all three occupancy model types. However, in all cases this covariate parameter was estimated with lower precision than that for the detection parameter (Table 3), providing little evidence for their effects on occupancy given this data set. For all three types of occupancy models, estimates of the probability of occupancy and detection from the best-supported model agreed very closely (Table 4). We evaluated the fit of the best-supported Mackenzie et al. (2002) occupancy model using a chi-square goodness-of-fit test (Fiske and Chandler 2011) and found no evidence for a lack of fit. Occupancy data are included in Text S3.
Model selection results for three types of single-season occupancy model for beach mice Peromyscus polionotus niveiventris on federal lands of the Kennedy Space Center, Cape Canaveral Air Force Station, and Canaveral National Seashore, Florida, surveyed in December 2009. Note that the log likelihood (LogLik) and associated Akaike information criterion (AIC) values for the Miller et al. (2011) model are on a different scale and are not directly comparable with those from the Royle and Link (2006) and MacKenzie et al. (2002) models.

Model average parameter and unconditional standard error estimates (SE) for three types of single-season occupancy models for beach mice Peromyscus polionotus niveiventris on federal lands of the Kennedy Space Center, Cape Canaveral Air Force Station, and Canaveral National Seashore, Florida, surveyed in December 2009. Model averaging was based on equation 6.12 of Burnham and Anderson (2002), excluding from the calculation any models in which the parameter was not included.

Parameter estimates for three types of single-season occupancy models for beach mice Peromyscus polionotus niveiventris on federal lands of the Kennedy Space Center, Cape Canaveral Air Force Station, and Canaveral National Seashore, Florida, surveyed in December 2009. The table gives for each model the estimate with the associated standard error (SE) and the 95% confidence interval (95% CI).

Discussion
False-positive detections from tracking tubes can severely bias occupancy estimates high, since what is being incorrectly measured is the occupancy of a combined population of more than just the target species (Royle and Link 2006; Fitzpatrick et al. 2009; McClintock et al. 2010). However, if this problem is accounted for, surveys using tracking tubes for small mammals such as the southeastern beach mouse are an efficient way to collect occupancy data over a wide geographic area. Several results from the occupancy modeling suggested that by using the reasonably conservative footprint width cutoff of 7.2 mm, the estimated rate of false positives was acceptably low in our study. First, parameter estimates from the Royle and Link (2006) model, which adjusts occupancy estimates for false positives, indicated that the probability of false detection was very low (Table 4). Second, occupancy and detection parameter estimates were similar for both the simple occupancy model and the models that allowed for false-positive detections. Finally, for all three types of occupancy models there was very similar support among models with various structures on the occupancy and detection parameters (Table 2), suggesting a low degree of unmodeled heterogeneity due to false detections. Taken together, this evidence shows that by eliminating the footprints that are at greatest risk to be misclassified, most of the beach mouse detections were correctly specified. These results demonstrate that using an empirically based cutoff width to discriminate between beach mice and cotton mice allowed the use of occupancy models that rely on certain detections (i.e., assume no false positives).
The Bayesian analysis of footprint widths also allowed us to describe regions of print widths in which we could be certain that a footprint belonged to a beach mouse, permitting the use of the Miller et al. (2011) model that takes advantage of the additional information regarding which prints were potentially misidentified. Surprisingly, this model also estimated a low rate of false positives, although it included as detections footprints beyond the range determined to definitely be beach mice. The logic of our choice of cutoff was conservative because it ignored the relative abundance of the two species; we implicitly assumed that any footprint encountered was equally likely to be of either species. However, we were sampling in areas more suitable for beach mice, so we wouldn't expect to encounter very many cotton mice. The Miller et al. (2011) model also allows the inclusion of covariates that inform about the degree of certainty for the remaining observations. This approach is well suited for occupancy studies of small mammal communities using tracking tubes, because it allows use of more of the information in the data collected. For example, habitat type, which may provide information about the proportion of beach mice vs. cotton mice at specific sites, could be included as a covariate on the rate of false occupancy. The use of such covariate information may be useful as we expand beach mouse habitat occupancy studies on our study site to areas with more overlap between species.
Our study estimated that beach mice occupied around 40% of the 10 km of primary dune on KSC in the center of the last remaining stronghold for the subspecies. Before our study an informal survey of local biologists' opinions on the expected rate of occupancy ranged from 0.05 to 0.90; thus our study refined knowledge of beach mouse habitat occupancy on the study site (Table 4). Since none of our models with covariates on the occupancy parameter was highly supported, we were not able to relate patterns in habitat occupancy with any ecological covariates. One reason for this may be a lack of variation among the sites in regard to the covariates measured, due to the limited geographic range sampled (10 km). A study is underway to sample a wider range of beach habitat along the entire 72 km of federal lands, designed to identify ecological covariates that explain patterns in beach mouse habitat occupancy.
The detection rate was estimated to be 0.23 (Table 4). Since we used spatial replication within sites to estimate detection probability (i.e., we deployed five tubes at each sample site and treated each tube as a replicate), this estimate corresponds to a per tube detection rate. The power to detect beach mice at a site if they were present can be calculated as: 1 − (1 − 0.23)5 = 0.73. In other words, we had a high power to detect beach mice at a site if they were present, based on the assumptions of our methods. One important assumption we made by using the tubes as spatial replicates was the independence in detection between tubes deployed at a site. If the probability that a beach mouse was detected by a tube within a site was related to that of the other tubes at the site, this would have biased our results. We believe that by spacing our tubes apart within sites, we were able to reduce correlation between detections. Results of a simulation providing evidence to support this claim are given in Text S4, and the R code to conduct such a simulation in Text S5.
In single-season habitat occupancy studies, it is important to be clear about what state variable is being measured. Possibilities range from habitat use integrated over the sampled time to habitat occupancy as a snapshot measurement (Efford and Dawson 2012). A key element in deciding the issue is often the effect of the scale of sampling relative to the animals' home range size. Our 9-m radius sample site was roughly 1,000 times smaller than a southeastern beach mouse home range as measured within and near our study area (Oddy et al. 1999, 2010). This places our state variable squarely in the realm of habitat use over the three-night sampling time frame. If interest was focused more on habitat occupancy than habitat use, a longer period of sampling could be used to allow more time for mice to encounter the tube array as they moved around within their habitat. We are conducting follow-up studies of beach mouse habitat occupancy to further explore this topic.
In summary, the use of an empirically determined cutoff width allowed adequate discrimination of beach mouse and cotton mouse footprints detected by tracking tubes for use in occupancy models, while avoiding potential bias due to misspecification (false detections). The Bayesian analysis of footprint widths of known animals provided a cutoff for footprint width that produced the desired low level of false-positive contamination rate. The Bayesian analysis also allowed us to describe regions of print width in which we could be very certain that a print belonged to a particular species, allowing use of the Miller et al. (2011) model that takes advantage of information about the rate of false positives. Together, these results demonstrated the utility of tracking tubes to efficiently sample habitat use and occupancy of beach mice, even in the presence of species with similar footprints.
Supplemental Material
Please note: The Journal of Fish and Wildlife Management is not responsible for the content or functionality of any supplemental material. Queries should be directed to the corresponding author for the article.
Text S1. R code for implementing a Bayesian hierarchical model of footprint widths incorporating individual random effects for beach mice Peromyscus polionotus niveiventri and cotton mice Peromyscus gossypinus captured on federal lands of the Kennedy Space Center, Cape Canaveral Air Force Station, and Canaveral National Seashore, Florida, May 2008 -February 2011.
Found at DOI: http://dx.doi.org/10.3996/032014-JFWM-025.S1 (5 KB R)
Text S2. Footprint widths for beach mice Peromyscus polionotus niveiventri and cotton mice Peromyscus gossypinus captured on federal lands of the Kennedy Space Center, Cape Canaveral Air Force Station, and Canaveral National Seashore, Florida, May 2008–February 2011. The data file is formatted to be sourced in R.
Found at DOI: http://dx.doi.org/10.3996/032014-JFWM-025.S2 (12 KB TXT)
Text S3. Data file containing footprint widths of beach mice Peromyscus polionotus niveiventri and cotton mice Peromyscus gossypinus measured during an occupancy survey on the Kennedy Space Center, Florida, conducted for three nights in December 2009. The file contains the footprint widths recorded at each of the five tracking tubes deployed within each of the 100 sites. The data file is formatted to be sourced in R.
Found at DOI: http://dx.doi.org/10.3996/032014-JFWM-025.S3 (2 KB TXT)
Text S4. Description of a computer simulation designed to test the survey design of a spatially replicated occupancy survey for beach mice Peromyscus polionotus niveiventri on the Kennedy Space Center, Florida, conducted for three nights in December 2009.
Found at DOI: http://dx.doi.org/10.3996/032014-JFWM-025.S4 (20 KB DOCX)
Text S5. R code to conduct a computer simulation designed to test the survey design of a spatially replicated occupancy survey for beach mice Peromyscus polionotus niveiventri on the Kennedy Space Center, Florida, conducted for three nights in December 2009.
Found at DOI: http://dx.doi.org/10.3996/032014-JFWM-025.S5 (2 KB R)
Figure S1. Box plots comparing the results of a computer simulation and the observed data for a spatially replicated occupancy survey for beach mice Peromyscus polionotus niveiventri on the Kennedy Space Center, Florida, conducted for three nights in December 2009.
Found at DOI: http://dx.doi.org/10.3996/032014-JFWM-025.S6 (3.6 MB TIF)
Reference S1. Ehrhart, LM. 1976. A study of diverse coastal ecosystem on the Atlantic coast of Florida: mammal studies. Final Report to NASA/KSC. Grant No. NGR10-019-004:1–182.
Found at DOI: http://dx.doi.org/10.3996/032014-JFWM-025.S7 (3.9 MB PDF)
Reference S2. Oddy DM, Gann SL, Stolen ED, Hall CR, Breininger DR. 2010. A summary of historic, long-term demography, radiotelemetry, dune restoration and occupancy studies of the southeastern beach mouse (Peromyscus polionotus niveiventris) on the John F. Kennedy Space Center, Florida. Report to NASA:1–116.
Found at DOI: http://dx.doi.org/10.3996/032014-JFWM-025.S8 (2.2 MB PDF)
Reference S3. Oddy DM. 2000. Population estimate and demography of the southeastern beach mouse (Peromyscus polionotus niveiventris) on Cape Canaveral Air Force Station, Florida. Master's thesis. Orlando: University of Central Florida.
Found at DOI: http://dx.doi.org/10.3996/032014-JFWM-025.S9 (1.4 MB PDF)
Reference S4. Stout IJ. 1979. Terrestrial community analysis. Volume 1 of IV: a continuation of baseline studies for environmentally monitoring space transportation systems (STS) at John F. Kennedy Space Center. NASA Contract Report 10-8986:1:628.
Found at DOI: http://dx.doi.org/10.3996/032014-JFWM-025.S10 (12.5 MB PDF)
Reference S5. Stout IJ, Roth JD, Parkinson CL, Van Zant JL, Kalkvik HM. 2004. A range wide evaluation of the impact of hurricane activity in 2004 on the status of the southeastern beach mouse. Final Report 2006–2008 for USFWS. Grant No. 240360121:182.
Found at DOI: http://dx.doi.org/10.3996/032014-JFWM-025.S11 (3.1 MB PDF)
Reference S6. Stout, IJ, Roth JD, Parkinson CL. 2007. The distribution and abundance of southeastern beach mouse (Peromyscus polionotus niveiventris) on the Cape Canaveral Air Force Station. Draft Final Report to Cape Canaveral Air Force Station. Grant No.: 240360121:166.
Found at DOI: http://dx.doi.org/10.3996/032014-JFWM-025.S12 (2.8 MB PDF)
Acknowledgments
We thank Lynne Phillips for support of our work at KSC, Tammy Foster for preparing the map for Figure 2, Dan Hunt for invaluable help with data management and processing, and numerous volunteers for assistance with fieldwork. We thank Ron Loggins, Bob Steidl, Brent Danielson, and two anonymous reviewers for many helpful comments on the manuscript. We thank Dave Miller for programming and advice on using the function occuFP, and Ian Fisk, R. Chandler and A. Royle for creating the unmarked package in R.
Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the U.S. Government.
References
Author notes
Stolen ED, Oddy DM, Legare ML, Breininger DR, Gann SL, Legare SA, Weiss SK, Holloway-Adkins KG, Schaub R. 2014. Preventing tracking tube false detections in occupancy modeling of southeastern beach mouse Peromyscus polionotus niveiventris. Journal of Fish and Wildlife Management 5(2):270–281; e1944-687X. doi: 10.3996/032014-JFWM-025
The findings and conclusions in this article are those of the author(s) and do not necessarily represent the views of the U.S. Fish and Wildlife Service.