Estimate Detection Probability Research Articles

Visual spectrogram scanning paired with an observation–confirmation occupancy model improves the efficiency and accuracy of bioacoustic anuran data

Passive acoustic monitoring using autonomous recording units has improved anuran amphibian call survey data collection. A challenge associated with this approach is the time required for audio data processing. Our objective was to develop a more efficient method of processing and analyzing acoustic data through visual spectrogram scanning and the application of an observation–confirmation occupancy model. We compared detection rates between methods of standard recording listening and visually scanning spectrogram images using different spectrogram parameters. Relative to listening, we found that 1 min spectrograms in two 30 s frames yield the best time efficiency–accuracy trade-off. A standard occupancy model applied to visual scanning data underestimated occupancy estimates relative to listening data for three species and overestimated occupancy for one species. The observation–confirmation model used a subset of listening data to improve the estimates of detection probability from visual scanning and therefore reduced bias in occupancy estimates when compared with using visual scanning data alone. Overall, the combination of the visual scanning method and the observation–confirmation model allowed us to maintain the accuracy of occupancy estimates while greatly increasing the efficiency of anuran data processing. These methods are widely applicable and can increase sample size and precision for acoustic monitoring programs using autonomous recording units.

A multi-species occupancy modeling approach to access the impacts of land use and land cover on terrestrial vertebrates in the Mumbai Metropolitan Region (MMR), Western Ghats, India.

Urbanization is one of the main drivers in the conversion of natural habitats into different land use and land cover types (LULC) which threaten the local as well as global biodiversity. This impact is particularly alarming in tropical countries like India, where ~18% of the world's population live, and its ever-growing economy (i.e., industrial development) expanded urban areas by several folds. We undertook this study to examine the impacts of urbanization (i.e., LULC) on terrestrial vertebrates (mammals, birds, reptiles, and amphibians) in the Mumbai Metropolitan Region (MMR), Western Ghats, India. We sampled different habitats ranged from highly disturbed urban areas to less disturbed forested areas. Multiple sampling methods such as quadrat sampling, line transect, point count, and camera trapping were used to quantify the target taxa. We used multi-species occupancy modeling in the Bayesian framework to estimate detection probability and occupancy and to assess the effect of various LULC on different species. All four groups showed a significant negative impact of increasing anthropogenic habitat cover on occupancy. Out of 213 species detected in this study, 96% of mammals, 85% of birds, 93.75% of amphibians, and 69.43% of reptiles showed a negative effect of anthropogenic habitat cover. Evidence suggests that historical and recent human disturbances could have played an important role in transforming this area from semi-evergreen and moist deciduous forest to open, scrubby, dry deciduous, and fire-prone landscape. This might be the reason for the high occupancy of open and degraded forest habitat preferring species in our study area. We recommend species-rich areas in the MMR, e.g., Karnala Bird Sanctuary (KBS) and Prabalgad-Matheran-Malanggad Hill Range (PMMHR), must be conserved through habitat restoration, ecotourism, public awareness, and policymaking.

Methods for estimating vital rates of greater sage‐grouse broods: a review

Biologists use a variety of methods to estimate productivity and resource selection of birds. The effectiveness and suitability of each method depends on the study's objectives, but is also influenced by many important traits, including detection probability, disturbance of focal birds and sampling frequency. We reviewed 504 greater sage‐grouse Centrocercus urophasianus papers published from 1990 to 2019 to document the most common brood survey methods used by investigators and summarized if and how they used brood survey data to estimate brood survival and detection probability. Of the 504 papers, 16.1% (n = 81) had useful information relevant to the review. The most common methods included daytime visual surveys (46.9%; n = 38), daytime flush surveys (33.3%; n = 27), nocturnal spotlight surveys (19.8%; n = 16), radio‐tagged chicks (16.0%; n = 13), wing surveys (9.9%; n = 8), brood routes (4.9%; n = 4) and pointing dogs (4.9%; n = 4). Fifty‐nine of the 81 papers used >1 method, only 2 of the 81 papers measured or reported detection probability, and none reported the level of disturbance caused by the method. Studies varied widely regarding the age of the brood when brood fate was confirmed (x̄ = 44.4 days post‐hatch, range 14–84 days). The frequency of brood sampling visits also varied greatly among studies (range = 1.19–3.85 surveys/brood/week) and this variation complicates comparison in fecundity and survival estimates across studies. Furthermore, 35 papers used >1 maternal behavior as purported indicators of brood fate, but none of them documented how accurate their indicators were. Future studies could reduce variance in estimates of sage‐grouse fecundity and brood survival by employing empirical methods to estimate detection probability, standardizing brood sampling methods and conducting trials to document the effects of hen or brood capture, handling and flushing on brood survival estimates. Moreover, the accuracy of commonly used indicators of brood fate, including maternal behaviors, flocking behavior and distance moved after flush needs verification.

A Combined Filter for Synchronous Detection in Underwater Acoustic Mobile Communication System

A scale-stretching combined filter is proposed for underwater acoustic mobile communication receivers. The combined filter consists of the sum of signals with different time stretching and shifting. Based on the matched filtering theory, Doppler stretching scales, time shift, and the order of each component of the combined filter are derived. The method proposed in this paper improves the matching degree of the filter with wideband Doppler echo signals with different moving speeds. Simulation results show that the combined filter proposed in this paper can improve the detection probability and synchronization time estimation accuracy of wideband Doppler echo. In addition, the combined filter proposed in this paper has the same calculation amount as the matched filter. This feature makes this filter suitable for the synchronous detection of underwater acoustic mobile communication with real-time operation and low power consumption requirements.

Detection probability and density estimation of fin whales by a seaglider

The effectiveness of gliders is evaluated for passive acoustic density estimation of fin whales. An estimate of the probability of detection as a function of range (or, equivalently, effective survey area) is required to estimate density from acoustic data collected by a single-hydrophone glider platform. A cabled hydrophone array was used to estimate fin whale localizations and tracks concurrently with a glider survey. Fin whale tracks were used as detection trials and a detection function for snapshots containing fin whale 20 Hz pulses recorded by the glider was modeled using a generalized additive model. Detection probability was strongly dependent on 40 Hz noise levels recorded on the glider. At the median noise level of 97 dB re 1μPa2/Hz, detection probability was near one at zero horizontal distance, and maximum detection range was near 40 km. The estimated effective survey area at this noise level was 870 km2. Using estimates of vocal rates and group size from tagged and tracked fin whales, respectively, the density was estimated as 2.4 fin whales per 1000 km2 (coefficient of variation 0.55). The framework presented here could be applied to other baleen whale species to advance the use of gliders for density estimation of cetaceans.

Adjusting a finite population block kriging estimator for imperfect detection

AbstractA finite population version of block kriging (FPBK) estimates a total or a mean when there is perfect detection of population units. However, many environmental datasets challenge the assumption of perfect detection. We consider two extensions of FPBK that incorporate imperfect detection. Spatial population estimator with detection: ratio then add (SPEDRA) adjusts observed counts by the estimated detection probability prior to spatial modeling. Spatial population estimator with detection: add then ratio (SPEDAR) uses spatial modeling on observed counts and then adjusts by mean detection probability. Unlike classical sampling approaches such as simple random sampling, SPEDRA and SPEDAR allow for spatial correlation among counts, and, being moment‐based, are less computationally intensive than a fully Bayesian model. Both SPEDRA and SPEDAR perform similarly in some simulation settings and give comparable estimates for a moose population total when applied to data from Togiak National Wildlife Refuge (AK). In settings where detection probability varies widely across sites, however, SPEDRA outperforms SPEDAR in reducing root mean square prediction error. We recommend SPEDRA in surveys with imperfect detection because it is more theoretically sound and generally performs better.

Maximizing detection probability for effective large‐scale nocturnal bird monitoring

AbstractAimOur specific objectives were to (a) estimate detection probabilities of nocturnal bird species, after taking into account survey‐specific covariates, and (b) investigate the influence of site‐specific covariates on owl and nightjar abundance, integrating effects of imperfect detection.InnovationWe conceived a survey protocol to estimate probabilities of detection and estimates of abundance of owls and nightjars in a large area, the Basque Country, northern Spain.Main ConclusionsOur results show that detection probability was strongly influenced by playback broadcast and by observer experience. Date irregularly affected species according to their reproductive periods, and we also found that vocal activity gradually diminished proportionally to the hour after sunset. Tawny owl (Strix aluco) was the most abundant and widely distributed species. Its abundance was positively related to forest areas (mainly pine timber forests) and decreased in large urban and agricultural areas. Open space species were less common. Barn owls (Tyto alba), little owls (Athene noctua), Eurasian scops owls (Otus scops) and long‐eared owls (Asio otus) avoided forest areas, but showed different responses to agriculture, grass‐fields, scrub and urban areas. Finally, European nightjar (Caprimulgus europaeus) was moderately frequent, and its abundance was favoured by scrub areas and, weakly, by eucalyptus patches, whereas it was negatively affected by large forest areas. We have shown that it is fundamental to consider the effects of survey‐specific covariates in the methodology design and analytical development. Our results also indicate some ecological adaptations and population changes in the nocturnal bird community following an increase in urbanization and in the extent of timber plantations, and also the simplification of natural habitats.

Status and Current Distribution of the Pine Barrens Treefrog (Hyla andersonii) in Florida

We conducted roadside call surveys at 111 historical Hyla andersonii (Pine Barrens Treefrog) sites in 2013–2016. We detected the species at 49 sites (44%), which is consistent with surveys conducted in the early 1980s. We detected the species throughout its historical range except Holmes County, which only has 4 historical sites. We also identified 33 new sites on public lands and 4 new sites on private lands. We used multi-season occupancy models to determine the influence of site and survey covariates on species occupancy and detection rates in Blackwater River State Forest. Species detection was positively associated with air temperature and partial cloud-cover and negatively associated with clear skies. Pine Barrens Treefrog occupancy rates were lower at survey sites surrounded by hardwood-dominated wetlands, suggesting that hardwood encroachment has negatively impacted this species on some areas of Blackwater River State Forest. The best model had an estimated detection probability of 0.43 (95% CI = 0.29–0.47) and an estimated occupancy of 0.63 (95% CI = 0.43–0.79). We recommend that future call surveys include a minimum of 5 visits to each survey site before inferring species absence. Our surveys suggest that the status and distribution of the species remain stable despite some habitat degradation.

Modelling the effect of covariates on the detectability and density of native blackbucks and invasive feral-horse using Multiple Covariate Distance Sampling at Point Calimere Wildlife Sanctuary, Southern India

Reliable estimates of population size and a knowledge of determinants of detectability and density estimates are crucial for effective conservation of species. Using Multiple Covariate Distance Sampling (MCDS), we modelled the influence of covariates on detection probability and density estimates of native blackbuck Antilope cervicapra and the invasive feral-horse Equus caballus at Point Calimere Wildlife Sanctuary. Grids of 1 × 1 km size were overlaid on the study area with a 1-km line transect in alternate grid cells. Sixteen transects were walked four times each, which detected 199 blackbuck and 152 feral-horse clusters. On each sighting, the climatic, habitat and anthropogenic covariates were recorded, which are likely to affect detection probability. At first, exploratory analyses were made using Conventional Distance Sampling (CDS) to arrive at estimates. Later, in Multiple Covariate Distance Sampling (MCDS), key models were fit into the dataset after selecting the potential covariates that had a significant effect on detection distances obtained from FAMD/PCA, and the best one was selected based on AIC. The MCDS analysis in blackbuck included covariates, viz., distance to water in the best model (29 individuals/km2; CI 22–36; detection probability = 0.58), followed by distance to feral-horse, sampling time and principal diet. The covariate distance to water emerged as the best model for feral-horse as well (13 individuals/km2; CI 9–18; detection probability = 0.36), followed by distance to cattle and principal diet. While the MCDS approach outperformed the CDS global and survey-strata estimates in blackbuck, both the approaches had a marginal difference in feral-horse. Post-stratification analysis showed that blackbuck density increased significantly with distance to water and feral-horse, but insignificantly with the absence of principal diet; whereas, the density of the feral-horse increased significantly with distance to water and cattle in the presence of principal diet. These findings suggest the ability of feral-horse to keep the blackbuck away from optimal areas, where the principal diet is abundant. Our study, thus, illustrates the need for the use of MCDS approach that ascertained (i) reliable population density estimates, (ii) spatiotemporal constraint on large herbivores caused by overabundance of water during the wet season, and (iii) competitive interaction of the invasive feral-horse with the native blackbuck and its likely effect on the latter keeping away from the former and the principal diet to overcome competition. Thus, the study highlights the impact of feral-horse on the native species and suggests measures for the long-term conservation of the blackbuck.

Observer performance and the effect of ambiguous taxon identification for fixed strip-width dugong aerial surveys

Aerial survey methods for census of wildlife populations are widely used to manage species. There has been considerable research to develop methods to cope with imperfect detection during aerial surveys, however misidentification remains an unresolved but significant issue. Using data from a comprehensive dugong aerial survey of the coastline of the Northern Territory, Australia, we assessed the influence of observer, sighting and environmental variables on probabilities of both observers in double-count, dual-observer teams detecting dugongs and dolphins (‘duplicate sighting probability’), the confidence with which observers could distinguish between dugongs and dolphins, and the reliability of post-detection observations by comparing data between observers. Dolphin duplicate sighting probability varied dependent on group size, Beaufort sea state and the lateral position inside the strip-width transect in relation to the aircraft. Dugong duplicate sighting probability varied across dual-observer teams. Counts of individuals in dugong and dolphin groups were unreliable past ≈5 individuals. Observer confidence in taxon identification varied by individual observer and throughout the duration of the survey (dolphin sightings) and potentially by the lateral position inside the transect strip-width in relation to the aircraft (dugong sightings). The probability of taxon identification disagreement between observers for duplicate dugong and dolphin sightings varied with group size, and markedly if one observer was uncertain (i.e. not 100% confident) of their assigned taxon. We believe this is predominately due to the presence of Australian snubfin dolphins (Orcaella heinsohni) in the survey area, which look like dugongs when seen from a distance, momentarily. We further show that application of different data filtering scenarios for uncertain taxonomic identifications and taxon identification disagreements between dual observers produces highly variable estimates of observer-specific dugong detection probability (ranging from 0.26 to 0.80 in a single observer) and dugong abundance (x̅ ± S.D., 40% ± 25%: difference between highest and lowest estimate, relative to the lowest estimate, across different data filtering scenarios). These results are particularly relevant not only to researchers conducting dugong aerial surveys, but also for other marine mammal aerial surveys in passing mode that target sympatric, morphologically similar species. We recommend development of operating procedures and analytical methods to quantify and adjust for misidentification and uncertain taxon identifications.

Fin whale 40‐Hz calling behavior studied with an acoustic tracking array

Fin whale 40‐Hz calling behavior studied with an acoustic tracking array

Evaluating the target‐tracking performance of scanning avian radars by augmenting data with simulated echoes

Abstract Small scanning radars have been used for many years to track the movements of insects, birds and bats. While the ability to track multiple flying animals simultaneously has numerous applications in basic ecology and applied conservation, translating radar tracks into accurate animal densities and fluxes requires estimates of detection and tracking probabilities. These can be challenging to determine, especially in environments with variable background clutter. In order to assess radar tracking probabilities, we added echoes from simulated bird tracks to sequences of scans collected with an X‐band marine radar at a colony of common and roseate terns (Sterna hirundo and S. dougallii) on Great Gull Island, New York, USA in the summers of 2014 and 2015. Automated detection, classification and tracking algorithms were used to extract the trajectories of terns from the radar data. The proportion of simulated tracks recovered by these procedures could then be used to estimate the tracking probabilities for real birds. Stationary telescope transects provided visual ground truth. The radar could track individual birds up to 3 km away, performing best between 0.5 and 1.2 km, where 38% of simulated birds were correctly detected and tracked in each scan. Overall, 94% of all simulated birds were tracked over at least part of their trajectories. Tracking performance was limited by weak bird echoes, backscatter from the sea surface and the inherent challenges of multi‐target tracking. This simulation‐based method provides a low‐cost, flexible approach for estimating radar‐tracking probabilities in complex, cluttered environments. Knowledge of these probabilities in turn allows the animal densities and fluxes to be corrected for imperfect detection. Despite their limitations, small scanning radars can track hundreds of birds simultaneously over tens of km2, giving a view of animal movement unavailable with other techniques.

Occurrence and Co‐Occurrence Patterns of Gar in River–Floodplain Habitats: Methods to Leverage Species Coexistence to Benefit Distributional Models

AbstractHabitat segregation and hypothesized biotic interactions among coexisting gar species may confound attempts to describe the distributions of these species by using only macrohabitat availability in the presence of conspecifics. However, the strength of interactions among gar species and the spatial scale at which they occur are largely unknown. We used an existing data set to evaluate the co‐occurrence patterns (i.e., random assemblages versus species co‐occurring more or less than expected at random) of three gar species in 62 dynamic river–floodplain habitats associated with the lower Mississippi River and its major tributaries. A novel parameterization of a multispecies occupancy model was utilized to examine the spatial relationships among the full array of possible gar assemblages across a gradient of floodplain habitats. Spotted Gar Lepisosteus oculatus were the most abundant and frequently encountered species (~78% of samples). Shortnose Gar L. platostomus (~27% of samples) and Longnose Gar L. osseus (~12% of samples) were relatively uncommon, and no Alligator Gar Atractosteus spatula were captured in over 600 electrofishing transects. Estimated detection probabilities of the encountered species varied (range = 0.27 [Longnose Gar] to 0.80 [Spotted Gar]), and five species‐specific environmental and sampling covariates predicted detection. Relatively strong co‐occurrence patterns between Shortnose Gar and Longnose Gar were significantly influenced by the proximity of a floodplain lake to a river (i.e., river : lake elevation change and linear distance) and by lake latitude. In contrast, the occurrence patterns of Spotted Gar were largely independent of the other species and had minor influences on the relationship between Longnose Gar and Shortnose Gar. We demonstrate how species co‐occurrence patterns can be leveraged to reduce uncertainty associated with species‐specific occupancy estimates and how species distribution models can be improved by utilizing abiotic and biotic features of the target ecosystems.

Codeless Acquisition of GNSS Signals

Theoretical characteristics of codeless GPS-signal acquisition in the L1 band are described and analyzed. The results obtained allow for a reliable choice of a coherent integration interval, calculation of signal detection thresholds, and estimation of signal detection probability. The operability and feasibility of the technique for codeless signal acquisition by frequency has been experimentally confirmed with the use of a software receiver.

Estimating Detection Probability for Burmese Pythons with Few Detections and Zero Recaptures

Detection has been a long-standing challenge to monitoring populations of cryptic herpetofauna, which often have detection probabilities that are closer to zero than to one. Burmese Pythons (Python bivittatus [=Python molurus bivittatus]), a recent invader in the Greater Everglades Ecosystem of Florida, are cryptic snakes that have long periods of inactivity. In addition, management actions such as removal of every python encountered create challenges for estimating population size and quantifying effects of management using traditional statistical approaches. We used Bayesian analysis of data collected from 59 visual surveys (144 person-surveys) covering a total distance of 485.6 km (1,185.1 person-km) and radiotelemetry to estimate detection probability for Burmese Pythons. These estimates can improve interpretation of encounter and removal data. We found that detection probability ranged from 0.0001 to 0.0146 depending on whether effort units accounted for total human effort across multiple surveyors and statistical method used. On the basis of our surveys, detection probabilities for Burmese Pythons are therefore likely <0.05, but factors such as the number of searchers or time of day may improve detection probability. Traditional capture–recapture or visual surveys are, however, unlikely to yield accurate information on Burmese Python population size or trends across time without cost-prohibitive effort. Consequently, novel methods development to monitor or measure Burmese Python populations, including techniques better equipped to handle very low detection, are critically needed for informative and reliable inferences about population size or the management effects of python removal.

Field evaluation of abundance estimates under binomial and multinomialN‐mixture models

Assessing and modelling abundance from animal count data is a very common task in ecology and management. Detection is arguably never perfect, but modern hierarchical models can incorporate detection probability and yield abundance estimates that are corrected for imperfect detection. Two variants of these models rely on counts of unmarked individuals, or territories (binomialN‐mixture models, orbinmix), and on detection histories based on territory‐mapping data (multinomialN‐mixture models ormultimix). However, calibration studies which evaluate these twoN‐mixture model approaches are needed. We analysed conventional territory‐mapping data (three surveys in 2014 and four in 2015) using both binmix and multimix models to estimate abundance for two common avian cavity‐nesting forest species (Great TitParus majorand Eurasian Blue TitCyanistes caeruleus). In the same study area, we used two benchmarks: occupancy data from a dense nestbox scheme and total number of detected territories. To investigate variance in estimates due to the territory assignment, three independent ornithologists conducted territory assignments. Nestbox occupancy yields a minimum number of territories, as some natural cavities may have been used, and binmix model estimates were generally higher than this benchmark. Estimates using the multimix model were slightly more precise than binmix model estimates. Depending on the person assigning the territories, the multimix model estimates became quite different, either overestimating or underestimating the ‘truth’. We conclude thatN‐mixture models estimated abundance reliably, even for our very small sample sizes. Territory‐mapping counts depended on territory assignment and this carried over to estimates under the multimix model. This limitation has to be taken into account when abundance estimates are compared between sites or years. Whenever possible, accounting for such hidden heterogeneity in the raw data of bird surveys, via including a ‘territory editor’ factor, is recommended. Distributing the surveys randomly (in time and space) to editors may also alleviate this problem.

Detection probabilities of bird carcasses along sandy beaches and marsh edges in the northern Gulf of Mexico

We estimated detection probabilities of bird carcasses along sandy beaches and in marsh edge habitats in the northern Gulf of Mexico to help inform models of bird mortality associated with the Deepwater Horizon oil spill. We also explored factors that may influence detection probability, such as carcass size, amount of scavenging, location on the beach, habitat type, and distance into the marsh. Detection probability for medium-sized carcasses (200–500 g) ranged from 0.82 (SE = 0.09) to 0.93 (SE = 0.04) along sandy beaches. Within sandy beaches, we found that intact/slightly scavenged carcasses were easier to detect than heavily scavenged ones and did not find strong effects of location on the beach on detection probability. We estimated detection rate for each combination of scavenging state, carcass size, and position along sandy beaches. In marsh edge habitats, detection ranged from 0.04 (SE = 0.04) to 0.86 (SE = 0.10), with detection rates rapidly increasing from small (< 200 g) to medium carcass sizes and leveling off between medium and extra-large (> 1000 g) carcasses regardless of vegetation type (Spartina or Phragmites). Carcasses of all sizes were generally harder to locate in Spartina-dominated marshes than in Phragmites-dominated ones. A subset of the data for which we could adequately assess the effect of distance into the marsh indicated that detection rates generally declined the farther a carcass was into marsh vegetation. Based on power analyses, our ability to identify predictors that influence detection rates would be higher with larger numbers of carcasses, greater numbers of search trials per carcass, or more balanced sampling distributions across predictor values.

Density-Dependent Escapement of Rusty Crayfish from Modified Minnow Traps with Varying Throat Configurations

Abstract Modified minnow traps are the most widely used gear for collecting tertiary burrowing crayfishes. The throats of modified minnow traps are often widened more than 60% to accommodate the capture of larger crayfish. However, widening this crucial chokepoint into the trap may facilitate easier escape of captured individuals, especially as density in the trap increases. Increased escapement rates may reduce catch rates and corresponding estimates of relative abundance and lower detection probability. Incorporating a design feature, that is, throat restriction, that allows entry of all sizes of crayfish while reducing escapement would be an improvement over current designs. Here, I present the results of a paired field and laboratory experiment comparing the effectiveness of modified minnow traps with a throat restriction (restricted) and without such a feature (unrestricted) under varying crayfish densities. I chose rusty crayfish Faxonius rusticus as a study organism because it is widespread and abundant in the Laurentian Great Lakes region and commonly the focus of research and removal efforts. Rusty crayfish capture and escapement were strongly influenced by throat design and crayfish densities. The field component demonstrated that both traps performed similarly under low-to-moderate densities; however, at high densities catch in unrestricted traps plateaued at approximately 50 crayfish/trap, while restricted traps kept accumulating catch up to 155 crayfish/trap. Laboratory trials demonstrated that escapement for both trap types was negligible at low density and slightly higher at medium density: 0.8% for restricted and 11.5% for unrestricted. However, at high density, escapement from restricted traps was 8.8 vs. 45.3% for unrestricted traps. Our findings suggest that inclusion of a throat restriction may increase catch of rusty crayfish by reducing escapement and may be of particular use in removal projects or when sampling in high-density populations.

Novel method for detection probability and estimating population size of mountain frog, Rana macrocnemis (Boulenger, 1885) at the end of its distribution range

Local amphibian populations at the edge of a species range are possibly of greater conservation concern than any other amphibians group. They experience greater demographic fluctuation than populations at the core of the range. We detected the most suitable distribution range of R. macrocnemis by maximum entropy (MaxEnt) method at the end of the southeastern edge of natural distribution range to find out which environmental variables have a significant role in determining the distribution pattern of this species in marginal populations. According to the map constructed, three important variables had a high contribution to species presence as land cover (63.4%), annual precipitation (27%), and precipitation of coldest quarter of the year (5.4%) variables. Then, we described new methods for estimating detection probability for terrestrial frogs, specifically R. macrocnemis. Finally, we estimated the population size of mountain frogs by calculated detection probability. Our repeated capture–re-capture (RCR) results suggest that the estimated detection probability for R. macrocnemis is: $$\widehat{p} = 0.052$$. Thus, the total average number of R. macrocnemis obtained from the 17 habitat sites is 982.5 adults (range: 708–1211 adults). In conclusion, the population estimates by detection probability index are generally much higher than densities reported for the Mountain frog populations than visual encounter estimation about 50.5 adults (range: 37–63 adults).

Estimating population size with imperfect detection using a parametric bootstrap

We develop a novel method of estimating population size from imperfectly detected counts of individuals and a separate estimate of detection probability. Observed counts are separated into classes within which detection probability is assumed constant. Within a detection class, counts are modeled as a single binomial observation X with success probability p where the goal is to estimate index N. We use a Horvitz–Thompson‐like estimator for N and account for uncertainty in both sample data and estimated success probability via a parametric bootstrap. Unlike capture–recapture methods, our model does not require repeated sampling of the population. Our method is able to achieve good results, even with small X. We show in a factorial simulation study that the median of the bootstrapped sample has small bias relative to N and that coverage probabilities of confidence intervals for N are near nominal under a wide array of scenarios. Our methodology begins to break down when P(X=0)&gt;0.1 but is still capable of obtaining reasonable confidence coverage. We illustrate the proposed technique by estimating (1) the size of a moose population in Alaska and (2) the number of bat fatalities at a wind power facility, both from samples with imperfect detection probabilities, estimated independently.