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An analytical solution for optimising detections when accounting for site establishment costs
Abstract
Indirect surveillance methods, such as remote cameras and acoustic monitoring, are increasingly used in ecological surveys. The time to deploy these devices includes initial setup, possible maintenance, retrieval and then a potentially large investment in the processing of the collected data. Thus, costs will increase with both the number of sites at which devices are deployed and the time they remain in the field, creating a trade-off between these factors when aiming to maximise the number of sites with detections.
Here we examine a scenario in which a target species occupies a proportion of the possible survey sites(psi), establishing a new site has a fixed cost (c), each survey of a site entails a cost per unit of survey effort (t), there is imperfect detection of the species during each survey such that the probability of failing to detect the species with a unit of survey effort is when the species is present, and there is a total budget that can be allocated to establishing and surveying sites (B). We show that the expected number of sites with detections is maximised by surveying each site with a particular amount of survey effort (v) that depends only on q and c. This analytical result can be used by researchers to optimise their survey effort prior to field work and provide opportunities for optimal allocation of their survey budget. We illustrate the method with an application to surveys of the threatened Leadbeater’s Possum (Gymnobelidus leadbeateri).
For many cryptic mammal species, limited distributional data restrict the scope or effectiveness of conservation actions, particularly in relation to habitat protection and/or management. The critically endangered Leadbeater’s possum illustrates this, with wet forests throughout its range impacted by logging and bushfire. The possum’s habitat has been subject to major disturbance and degradation over recent decades; however, the cryptic behaviour of the species has meant population trajectories have been difficult to monitor. Since 2012, surveys for the possum have been greatly expanded, predominantly based around camera trapping. This paper examines outcomes following a decade of targeted camera trapping for this high-profile threatened species. There have been 1143 camera trapping detections of Leadbeater’s possum since 2012, representing 57% of all detections over this period. For comparison, there were just 274 detections of the species over a comparable period during the preceding decade using all other survey techniques. The substantial increase in records reflects greater survey effort, but also the effectiveness of baited camera traps at detecting this cryptic mammal. As a consequence, we have greatly improved understanding of the species’ distribution within its core range following major bushfire in 2009. These detection data have informed some aspects of forest management, including the establishment of small logging exclusion areas. Other applications of camera traps have included directing them at dens, providing a non-invasive means of monitoring translocated individuals and reproductive success. Several important caveats regarding camera trapping surveys are discussed, particularly that detection/non-detection data may be insensitive at detecting population declines for communally-denning species such as Leadbeater’s possum, where abundance may change more readily than occupancy. A risk accompanying the proliferation of camera trapping is over-reliance on rapid, one-off camera surveys that fail to provide the in-depth insights on demography and population dynamics required to inform effective management of threatened species. This case study highlights the importance of robust survey and monitoring data to inform species conservation planning and management. The results also demonstrate that camera trapping can be as effective and efficient in determining occupancy for some arboreal mammals as it is for terrestrial species, where it is more commonly applied.
Occupancy models are used in statistical ecology to estimate species dispersion. The two components of an occupancy model are the detection and occupancy probabilities, with the main interest being in the occupancy probabilities. We show that for the homogeneous occupancy model there is an orthogonal transformation of the parameters that gives a natural two-stage inference procedure based on a conditional likelihood. We then extend this to a partial likelihood that gives explicit estimators of the model parameters. By allowing the separate modelling of the detection and occupancy probabilities, the extension of the two-stage approach to more general models has the potential to simplify the computational routines used there.
The development and use of automated species detection technologies, such as acoustic recorders, for monitoring wildlife are rapidly expanding. Automated classification algorithms provide cost‐ and time‐effective means to process information‐rich data, but often at the cost of additional detection errors. Appropriate methods are necessary to analyse such data while dealing with the different types of detection errors.
We developed a hierarchical modelling framework for estimating species occupancy from automated species detection data. We explore design and optimization of data post‐processing procedures to account for detection errors and generate accurate estimates. Our proposed method accounts for both imperfect detection and false‐positive errors and utilizes information about both occurrence and abundance of detections to improve estimation.
Using simulations, we show that our method provides much more accurate estimates than models ignoring the abundance of detections. The same findings are reached when we apply the methods to two real datasets on North American frogs surveyed with acoustic recorders.
When false positives occur, estimator accuracy can be improved when a subset of detections produced by the classification algorithm is post‐validated by a human observer. We use simulations to investigate the relationship between accuracy and effort spent on post‐validation, and found that very accurate occupancy estimates can be obtained with as little as 1% of data being validated.
Automated monitoring of wildlife provides opportunity and challenges. Our methods for analysing automated species detection data help to meet key challenges unique to these data and will prove useful for many wildlife monitoring programmes.
Most species are imperfectly detected during biological surveys, which creates uncertainty around their abundance or presence at a given location. Decision makers managing threatened or pest species are regularly faced with this uncertainty. Wildlife diseases can drive species to extinction; thus, managing species with disease is an important part of conservation. Devil facial tumor disease (DFTD) is one such disease that led to the listing of the Tasmanian devil (Sarcophilus harrisii) as endangered. Managers aim to maintain devils in the wild by establishing disease‐free insurance populations at isolated sites. Often a resident DFTD‐affected population must first be removed. In a successful collaboration between decision scientists and wildlife managers, we used an accessible population model to inform monitoring decisions and facilitate the establishment of an insurance population of devils on Forestier Peninsula. We used a Bayesian catch‐effort model to estimate population size of a diseased population from removal and camera trap data. We also analyzed the costs and benefits of declaring the area disease‐free prior to reintroduction and establishment of a healthy insurance population. After the monitoring session in May–June 2015, the probability that all devils had been successfully removed was close to 1, even when we accounted for a possible introduction of a devil to the site. Given this high probability and the baseline cost of declaring population absence prematurely, we found it was not cost‐effective to carry out any additional monitoring before introducing the insurance population. Considering these results within the broader context of Tasmanian devil management, managers ultimately decided to implement an additional monitoring session before the introduction. This was a conservative decision that accounted for uncertainty in model estimates and for the broader nonmonetary costs of mistakenly declaring the area disease‐free.
The challenges associated with monitoring low‐density carnivores across large landscapes have limited the ability to implement and evaluate conservation and management strategies for such species. Non‐invasive sampling techniques and advanced statistical approaches have alleviated some of these challenges and can even allow for spatially explicit estimates of density, one of the most valuable wildlife monitoring tools.
For some species, individual identification comes at no cost when unique attributes (e.g. pelage patterns) can be discerned with remote cameras, while other species require viable genetic material and expensive laboratory processing for individual assignment. Prohibitive costs may still force monitoring efforts to use species distribution or occupancy as a surrogate for density, which may not be appropriate under many conditions.
Here, we used a large‐scale monitoring study of fisher Pekania pennanti to evaluate the effectiveness of occupancy as an approximation to density, particularly for informing harvest management decisions. We combined remote cameras with baited hair snares during 2013–2015 to sample across a 70 096‐km ² region of western New York, USA . We fit occupancy and Royle–Nichols models to species detection–non‐detection data collected by cameras, and spatial capture–recapture (SCR) models to individual encounter data obtained by genotyped hair samples. Variation in the state variables within 15‐km ² grid cells was modelled as a function of landscape attributes known to influence fisher distribution.
We found a close relationship between grid cell estimates of fisher state variables from the models using detection–non‐detection data and those from the SCR model, likely due to informative spatial covariates across a large landscape extent and a grid cell resolution that worked well with the movement ecology of the species. Fisher occupancy and density were both positively associated with the proportion of coniferous‐mixed forest and negatively associated with road density. As a result, spatially explicit management recommendations for fisher were similar across models, though relative variation was dampened for the detection–non‐detection data.
Synthesis and applications . Our work provides empirical evidence that models using detection–non‐detection data can make similar inferences regarding relative spatial variation of the focal population to models using more expensive individual encounters when the selected spatial grain approximates or is marginally smaller than home range size. When occupancy alone is chosen as a cost‐effective state variable for monitoring, simulation and sensitivity analyses should be used to understand how inferences from detection–non‐detection data will be affected by aspects of study design and species ecology.
Countries committed to implementing the Convention on Biological Diversity's 2011–2020 strategic plan need effective tools to monitor global trends in biodiversity. Remote cameras are a rapidly growing technology that has great potential to transform global monitoring for terrestrial biodiversity and can be an important contributor to the call for measuring Essential Biodiversity Variables. Recent advances in camera technology and methods enable researchers to estimate changes in abundance and distribution for entire communities of animals and to identify global drivers of biodiversity trends. We suggest that interconnected networks of remote cameras will soon monitor biodiversity at a global scale, help answer pressing ecological questions, and guide conservation policy. This global network will require greater collaboration among remote-camera studies and citizen scientists, including standardized metadata, shared protocols, and security measures to protect records about sensitive species. With modest investment in infrastructure, and continued innovation, synthesis, and collaboration, we envision a global network of remote cameras that not only provides real-time biodiversity data but also serves to connect people with nature.
Conservation of threatened species relies on predictions about their spatial distribution; however, it is often difficult to detect species in the wild. The combination of acoustic monitoring to improve species detectability and statistical methods to account for false‐negative detections can improve species distribution estimates.
Here, we combine a novel automated species‐specific identification approach with occupancy models that account for imperfect detectability to provide a more accurate species distribution map of the Elfin Woods Warbler Setophaga angelae , a rare, elusive and threatened bird species. We also compared three automated species identification/validation approaches to determine which approach provided occupancy estimates similar to manual validation of all recordings. Acoustic data were collected along three elevational gradients (95–1074 m a.s.l) in El Yunque National Forest, Puerto Rico. The detection matrices acquired through automated species‐specific identification models and manual validations of all recordings were used to create occupancy models.
Although this species has a wider distribution than previously reported, it depends on Palo Colorado forest cover and it mainly occurs between 600 and 900 m a.s.l. Unbiased and precise occupancy models were developed by using automated species identification models and only manually validating 4% of the recordings.
Our approach draws on the strength of two active areas of ecological research: acoustic monitoring and occupancy modelling. Our methods provide an effective and efficient way to translate the enormous amount of acoustic information collected with passive acoustic monitoring devices into meaningful ecological data that can be applied to understand and map the distribution of rare, elusive and threatened species.
Previous studies that optimize allocation of surveillance resources over space have assumed that detection rates are constant over time and that travel or survey costs are the same for all sites. Other recent research explicitly accounts for stochastically varying detection rates and distinct travel costs but restricts attention to the optimal number of visits to a single site. Here, we integrate these approaches to construct a model that optimizes the allocation of surveillance effort over both space and time.
The solution defines the budget that should be allocated to each site and the number of visits over which that search budget should be expended. We show that the solution has close affinities with that of Hauser and McCarthy (Ecology Letters, 12, 2009, 683), which ignored temporal variation in detection rates and travel costs. We illustrate our approach by finding the optimal allocation of survey effort over space and time that maximizes the expected number of detections of the cascade treefrog ( Litoria pearsoniana ) in a region.
In deriving our model, we also solve an alternative model to Moore et al . (PLoS One, 9, 2014) that considers the trade‐off between the number of visits and length of each visit when the detection rate at a site varies over time. We compare the predictions of the original model of Moore et al . (PLoS One, 9, 2014) and the new model using experimental data on detections of two species, showing the two models perform similarly well.
Interestingly, when variable detection rates and travel costs are considered using our model, the form of the resulting objective function is very similar to the case in which they are ignored; in both cases, the probability of failed detection at each site is a negative exponential function of effort. However, travel costs impose a discontinuity into the solution space making the decision variables semi‐continuous (i.e. the optimal surveillance effort at each site is either zero or a value greater than the travel cost). This discontinuity complicates the task of finding the optimal solution. We propose a straightforward algorithm that finds very good approximate solutions.
The occurrence of false positive detections in presence–absence data, even when they occur infrequently, can lead to severe bias when estimating species occupancy patterns. Building upon previous efforts to account for this source of observational error, we established a general framework to model false positives in occupancy studies and extend existing modeling approaches to encompass a broader range of sampling designs. Specifically, we identified three common sampling designs that are likely to cover most scenarios encountered by researchers. The different designs all included ambiguous detections, as well as some known-truth data, but their modeling differed in the level of the model hierarchy at which the known-truth information was incorporated (site level or observation level). For each model, we provide the likelihood, as well as R and BUGS code needed for implementation. We also establish a clear terminology and provide guidance to help choosing the most appropriate design and modeling approach.
The survey of plant and animal populations is central to undertaking field ecology. However, detection is imperfect, so the absence of a species cannot be determined with certainty. Methods developed to account for imperfect detectability during surveys do not yet account for stochastic variation in detectability over time or space. When each survey entails a fixed cost that is not spent searching (e.g., time required to travel to the site), stochastic detection rates result in a trade-off between the number of surveys and the length of each survey when surveying a single site. We present a model that addresses this trade-off and use it to determine the number of surveys that: 1) maximizes the expected probability of detection over the entire survey period; and 2) is most likely to achieve a minimally-acceptable probability of detection. We illustrate the applicability of our approach using three practical examples (minimum survey effort protocols, number of frog surveys per season, and number of quadrats per site to detect a plant species) and test our model's predictions using data from experimental plant surveys. We find that when maximizing the expected probability of detection, the optimal survey design is most sensitive to the coefficient of variation in the rate of detection and the ratio of the search budget to the travel cost. When maximizing the likelihood of achieving a particular probability of detection, the optimal survey design is most sensitive to the required probability of detection, the expected number of detections if the budget were spent only on searching, and the expected number of detections that are missed due to travel costs. We find that accounting for stochasticity in detection rates is likely to be particularly important for designing surveys when detection rates are low. Our model provides a framework to do this.
Setting up effective conservation strategies requires the precise determination of the targeted species’ distribution area and, if possible, its local abundance. However, detection issues make these objectives complex for most vertebrates. The detection probability is usually <1 and is highly dependent on species phenology and other environmental variables. The aim of this study was to define an optimized survey protocol for the Mediterranean amphibian community, that is, to determine the most favorable periods and the most effective sampling techniques for detecting all species present on a site in a minimum number of field sessions and a minimum amount of prospecting effort. We visited 49 ponds located in the Languedoc region of southern France on four occasions between February and June 2011. Amphibians were detected using three methods: nighttime call count, nighttime visual encounter, and daytime netting. The detection nondetection data obtained was then modeled using site-occupancy models. The detection probability of amphibians sharply differed between species, the survey method used and the date of the survey. These three covariates also interacted. Thus, a minimum of three visits spread over the breeding season, using a combination of all three survey methods, is needed to reach a 95% detection level for all species in the Mediterranean region. Synthesis and applications: detection nondetection surveys combined to site occupancy modeling approach are powerful methods that can be used to estimate the detection probability and to determine the prospecting effort necessary to assert that a species is absent from a site.
Motion-activated cameras are a versatile tool that wildlife biologists can use for sampling wild animal populations to estimate species occurrence. Occupancy modelling provides a flexible framework for the analysis of these data; explicitly recognizing that given a species occupies an area the probability of detecting it is often less than one. Despite the number of studies using camera data in an occupancy framework, there is only limited guidance from the scientific literature about survey design trade-offs when using motion-activated cameras. Our aim was to provide a fuller understanding of these trade-offs to enable researchers with varying backgrounds in ecological modelling and statistics to maximize available resources and determine whether the objectives of a monitoring program or research study are achievable. We use an empirical dataset collected from 40 cameras deployed across 160 km2 of the Western Slope of Colorado, USA. Specifically, we use these empirical data to estimate species occupancy and detection parameters from motion-activated cameras that are then used in a simulation exercise. This approach provides a clear link between field data and the simulations that explore how survey effort (number of cameras deployed and the length of sampling period) affects the accuracy and precision (i.e. error) of the occupancy estimate for ten mammal and three virtual species. A total of 54 survey designs were considered by varying combinations of sites (10-120 cameras) and occasions (20-120 survey days). Our findings demonstrate that increasing total sampling effort generally decreases error associated with the occupancy estimate, but changing the number of sites or sampling duration can have very different results, depending on whether a species is spatially common or rare (occupancy = ψ) and easy or hard to detect when available (detection probability = p). For rare species with a low probability of detection (i.e., raccoon and spotted skunk) the required survey effort includes increasing the number of sites and the number of survey days, often to a level that may be logistically unrealistic for many studies. For common species with low detection (i.e., bobcat and coyote) the most efficient sampling approach was to increase the number of occasions (survey days). However, for common species that are moderately detectable (i.e., cottontail rabbit and mule deer), occupancy could reliably be estimated with comparatively low numbers of cameras over a short sampling period. We provide general guidelines for reliably estimating occupancy across a range of terrestrial species (rare to common: ψ = 0.175-0.970, and low to moderate detectability: p = 0.003-0.200) using motion-activated cameras. Results from our study have wide applicability to camera studies conducted across a range of environments and taxa, which can be used by wildlife researchers/managers with limited knowledge of the relative abundance and likelihood of detection of a particular species. We emphasize the importance of prior biological knowledge, defined objectives and detailed planning (e.g. simulating different study-design scenarios) for designing effective monitoring programs and research studies.
Many monitoring programmes are successful at monitoring common species, whereas rare species, which are often of highest conservation concern, may be detected infrequently. Study designs that increase the probability of detecting rare species at least once over the study period, while collecting adequate data on common species, strengthen programme ability to address community‐wide hypotheses about how an ecosystem functions or responds to management actions. Study design guidelines exist for single‐species occupancy models, but practical guidance for monitoring species communities is needed. Single‐species population‐level designs are necessarily optimal for targeted species, whereas community study designs may be optimal for the assemblage of species, but not for every species within the community. Our objective was to provide a general optimization tool for multi‐species models and to illustrate this tool using data from two avian community studies.
We conducted a simulation study with a B ayesian hierarchical model to explore design and cost trade‐offs for avian community monitoring programmes. We parameterized models using two long‐term avian studies from A rizona, USA and evaluated bias and accuracy for different combinations of species in the regional species pool and sampling design combinations of number of sites and sampling occasions. We optimized for maximum accuracy of species richness, detection probability and occupancy probability of rare species, given a fixed budget.
Statistical properties for species richness and detection probability of species within the community were driven more by sampling occasions, whereas rare species occupancy probability was influenced more by percentage of area sampled. These results are consistent with results from single‐species models, suggesting some similarities between community‐level and single‐species models with occupancy and detection.
Synthesis and applications . Study designs must be cost‐efficient while providing reliable knowledge. Researchers and managers have limited funds for collecting data. Our template can be used by researchers and managers to evaluate trade‐offs and efficiencies for allocating samples between the number of occasions and sites in multi‐species studies, and allow them to identify the optimal study design in order to achieve specific study objectives.
Problems formulated in terms of logarithmic or exponential equations often
use the Lambert W function in their solutions. Expansions, approximations and
bounds on W have been derived in an effort to gain a better understanding of
the relationship between equation parameters. In this paper, we focus on one of
the branches of W, denoted as , we derive tractable upper and lower
bounds and we illustrate their usefulness in identifying conditions under which
user cooperation can yield a lower outage probability than non-cooperative
transmission.
Much research has centered on determining which habitat model best predicts species occurrence. However, previous work typically used data sets that are inherently biased for evaluation. The use of simulated data provides a way of testing model performance using un-biased data where the true relationships between species occurrence and population processes are predefined using sound ecological theory. We used a process-based habitat model to generate simulated occurrence data to evaluate presence–absence and presence–only methods: generalized linear and generalized additive models (GLM, GAM), maximum entropy model (Maxent), and discrete choice models (DCM). This is the first study to use a DCM for predicting species distributions. We varied the effect that habitat quality had on fecundity and reported the model responses to these changes. When the effect of habitat quality on fecundity was weak, model performance was no better than random for all methods, however, performance increased as the habitat/fecundity relationship became stronger. For each level of habitat quality effect, there was little variation in performance between the presence–absence and presence–only methods. The use of a process-based habitat model to generate occurrence data for evaluating model performance has a distinct advantage over other testing methods, because no errors are made during sampling and the true ecological relationships between population process and species occurrence are known. This leads to un-biased results and increased confidence in assessing model performance and making management recommendations.
Nondetection of a species at a site does not imply that the species is absent unless the probability of detection is 1. We propose a model and likelihood-based method for estimating site occupancy rates when detection probabilities are 1. The model provides a flexible framework enabling covariate information to be included and allowing for missing observations. Via computer simulation, we found that the model provides good estimates of the occupancy rates, generally unbiased for moderate detection probabilities (0.3). We estimated site occupancy rates for two anuran species at 32 wetland sites in Maryland, USA, from data collected during 2000 as part of an amphibian monitoring program, Frog-watch USA. Site occupancy rates were estimated as 0.49 for American toads (Bufo amer-icanus), a 44% increase over the proportion of sites at which they were actually observed, and as 0.85 for spring peepers (Pseudacris crucifer), slightly above the observed proportion of 0.83.
Invasive species surveillance has typically been targeted to where the species is most likely to occur. However, spatially varying environmental characteristics and land uses may affect more than just the probability of occurrence. Biodiversity or economic value, and the ease of detection and control are also likely to vary. We incorporate these factors into a detection and treatment model of a low-density invader to determine the surveillance strategy that minimizes expected management costs. Sites with a high probability of invader occurrence and great benefits associated with detection warrant intensive surveillance; however, the optimum investment is a nonlinear function of these factors. Environments where the invader is relatively easy to detect are prioritized for surveillance, although only a moderate investment is necessary to ensure a high probability of detection. Intensive surveillance effort may be allocated to other sites if the probability of occurrence, budget and/or expected benefits is sufficiently high.
Measuring population changes and trends is essential to identify threatened species, and is requested by several environmental regulations (e.g. European Habitat Directive). However, obtaining this information for small and cryptic animals is challenging, and requires complex, broad-scale monitoring schemes. How should we allocate the limited resources available for monitoring, to maximize the probability of detecting declines? The analysis of simulated data can help to identify the performance of monitoring scenarios across species with different features. We simulated data of populations with a wide range of abundance, detection probability
and rate of decline, and tested under which circumstances open-population N-mixture models can successfully detect the decline of populations. We tested multiple monitoring strategies, to identify the ones having the highest probability of detecting declines. If 30 sites are surveyed, strong declines (≥30%) can be successfully
spotted for nearly all the simulated species, except the species with lowest abundance and detection probability. Weaker declines are successfully identified only in species that are easy to detect and have high abundance. Increasing the number of sites quickly increases model power, but hundreds of sites would require monitoring to measure trends of the least detectable species. For most of species, performance of monitoring was improved by: surveying many sites with a few replicates per site; surveying many small sites instead of a few large sites; combining data from sites monitored for multiple species. Our findings show that one single monitoring
approach cannot be appropriate for all the species, and that surveying efforts should be modulated across them, according to their detection probabilities and abundances. We provide quantitative values on how the number of surveys and the number of sites to be surveyed can be assigned to different species, and emphasize
the need of planning to maximize the performance of monitoring.
Occupancy‐detection models that account for imperfect detection have become widely used in many areas of ecology. As with any modelling exercise, it is important to assess whether the fitted model encapsulates the main sources of variation in the data, yet there have been few methods developed for occupancy‐detection models that would allow practitioners to do so.
In this paper, a new type of residual for occupancy‐detection models is developed according to the method of Dunn & Smyth ( Journal of Computational and Graphical Statistics , 5 , 1996, 236–244). Residuals are separately constructed to diagnose the occupancy and detection components of the model.
Because the residuals are quite noisy, we suggest fitting a smoother through plots of residuals against predictors of fitted values, with 95% confidence bands, to diagnose lack‐of‐fit.
The method is illustrated using Swiss squirrel data, and evaluated using simulations based on that dataset.
Plotting residuals against predictors or against fitted values performed reasonably well as methods for diagnosing violations of occupancy‐detection model assumptions, particularly plots of residuals against a missing predictor. Relatively high false positive rates were sometimes observed, but this seems to be controlled reasonably well by fitting smoothers to these plots and being guided in interpretation by 95% confidence bands around the smoothers.
Species occupancy, the proportion of sites occupied by a species, is a state variable of interest in ecology. One challenge in its estimation is that detection is often imperfect in wildlife surveys. As a consequence, occupancy models that explicitly describe the observation process are becoming widely used in the discipline. These models require data that are informative about species detectability. Such information is often obtained by conducting repeat surveys to sampling sites. One strategy is to survey each site a predefined number of times, regardless of whether the species is detected. Alternatively, one can stop surveying a site once the species is detected and reallocate the effort saved to surveying new sites. In this paper we evaluate the merits of these two general design strategies under a range of realistic conditions. We conclude that continuing surveys after detection is beneficial unless the cumulative probability of detection at occupied sites is close to one, and that the benefits are greater when the sample size is small. Since detectability and sample size tend to be small in ecological applications, our recommendation is to follow a strategy where at least some of the sites continue to be sampled after first detection.
Camera-traps are increasingly used to survey threatened mammal species and are an important tool for estimating habitat occupancy. To date, cost-efficient occupancy survey effort allocation studies have focused on trade-offs between number of sample units (SUs) and sampling occasions, with simplistic accounts of associated costs which do not reflect camera-trap survey realities. Here we examine camera-trap survey costs as a function of the number of SUs, survey duration and camera-traps per SU, linking costs to precision in occupancy estimation. We evaluate survey effort trade-offs for hypothetical species representing different levels of occupancy (ψ) and detection (p) probability to identify optimal design strategies. We apply our cost function to three threatened species as worked examples. Additionally, we use an extensive camera-trap data set to evaluate independence between multiple camera traps per SU. The optimal number of sampling occasions that result in minimum cost decrease as detection probability increases, irrespective of whether the species is rare (ψ < 0.25) or common (ψ > 0.5). The most expensive survey scenarios occur for elusive (p < 0.25) species with a large home range (> 10 km²), where the survey is conducted on foot. Minimum survey costs for elusive species can be achieved with fewer sampling occasions and multiple cameras per SU. Multiple camera-traps set within a single SU can yield independent species detections. We provide managers and researchers with guidance for conducting cost-efficient camera-trap occupancy surveys. Efficient use of survey budgets will ultimately contribute to the conservation of threatened and data deficient mammals.
Recently, estimators have been developed to estimate occupancy probabilities when false‐positive detections occur during presence–absence surveys. Some of these estimators combine different types of survey data to improve estimates of occupancy. With these estimators, there is a trade‐off between the number of sample units surveyed, and the number and type of surveys at each sample unit. Guidance on efficient design of studies when false positives occur is unavailable.
For a range of scenarios, I identified survey designs that minimized the mean square error of the estimate of occupancy. I considered an approach that uses one survey method and two observation states and an approach that uses two survey methods. For each approach, I used numerical methods to identify optimal survey designs when model assumptions were met and parameter values were correctly anticipated, when parameter values were not correctly anticipated and when the assumption of no unmodelled detection heterogeneity was violated.
Under the approach with two observation states, false‐positive detections increased the number of recommended surveys, relative to standard occupancy models. If parameter values could not be anticipated, pessimism about detection probabilities avoided poor designs. Detection heterogeneity could require more or fewer repeat surveys, depending on parameter values. If model assumptions were met, the approach with two survey methods was inefficient. However, with poor anticipation of parameter values, with detection heterogeneity or with removal sampling schemes, combining two survey methods could improve estimates of occupancy.
Ignoring false positives can yield biased parameter estimates, yet false positives greatly complicate the design of occupancy studies. Specific guidance for major types of false‐positive occupancy models, and for two assumption violations common in field data, can conserve survey resources. This guidance can be used to design efficient monitoring programmes and studies of species occurrence, species distribution or habitat selection, when false positives occur during surveys.
Building useful models of species distributions requires attention to several important issues, one being imperfect detection of species. Data sets of species detections are likely to suffer from false absence records. Depending on the type of survey, false positive records can also be a problem. Disregarding these observation errors may lead to important biases in model estimation as well as overconfidence about precision. The severity of the problem depends on the intensity of these errors and how they correlate with environmental characteristics (e.g. where species detectability strongly depends on habitat features). A powerful modelling framework that accounts for imperfect detection in the modelling of species distributions has developed in the last 10-15 years. Fundamental to this framework is that data must be collected in a way that is informative about the observation process. For instance, such data can be in the form of multiple detection/non-detection records obtained from several visits/observers/detection methods at (at least) some of the sites, or from data on times to detection within a survey visit. The framework can extend to studying species' range dynamics and the modelling of communities, as well as approaches for analysing data on abundance and multiple occupancy states (rather than binary presence/absence). This paper summarizes these modelling advances, discusses evidence about effects of imperfect detection and the difficulties of working with it, and concludes with the current outlook for future research and application of these methods. This article is protected by copyright. All rights reserved.
Aim
We assessed the influence of species non-detection in modelling species distributions with an ensemble consensus approach that did not account for imperfect detection, compared with an occupancy model that did.
Location
The hydrographic network of France.
Methods
We compared range maps of 35 stream fish species with differing degrees of detectability predicted using a consensus approach combining eight species distribution models (SDMs) to maps produced using an occupancy model. Using a spatially and temporally extensive monitoring database of fish populations (France), we modelled the occurrence of species as a function of several climatic and habitat variables and projected species distributions across the whole of the French hydrographic network. The benefits of occupancy models were then assessed from the differences in both predictive performance and species distribution.
Results
We found that although the occupancy models enhanced the performance for difficult to detect species, consensus models outperformed occupancy models for highly detectable species. In contrast to the minor differences observed in performance measures, estimates of species distributions were severely affected by whether or not imperfect detection was accounted for and varied linearly according to species detectability.
Main conclusions
This study demonstrated that false absences could have major consequences in estimating species distribution ranges. However, accounting for imperfect detection may not be enough to improve conventional SDMs. These findings could have important implications for conservation, notably in developing large-scale distribution models and documenting species range shifts in the context of recent climate change.
1. Occupancy is an important concept in ecology. To obtain an unbiased estimator of occupancy it is necessary to address the issue of imperfect detection, which requires conducting replicate surveys at the sites being sampled. As the allocation of total effort can be done in different ways, occupancy studies should be designed carefully to ensure an efficient use of available resources.
2. In this paper we address the design of single-season single-species occupancy studies with a focus on: (1) issues relating to small sample sizes and (2) the potential relevance of including the precision of the detectability estimator as a criterion for design. We explore analytically the model with constant probabilities and examine how bias and precision are affected by the numbers of sites and replicates used.
3. We show how, for small sample sizes, the estimator properties depart from those predicted by large sample approximations, emphasize the need to use simulations when designing for small sample sizes and provide a new software tool that can assist in this process.
4. We offer advice on the amount of replication needed when the probability of detection is a quantity of interest and show that, in this case, it is more efficient to reduce the number of sites and increase the amount of replication per site compared with situations where only occupancy is of concern.
5. Synthesis and applications. It is essential to have clearly stated objectives before starting a study and to design the sampling accordingly. As the allocation of effort into replication and sites can be done in different ways, occupancy studies should be designed carefully to ensure an efficient use of available resources. To avoid waste, it is crucial to anticipate the quality of the estimates that can be expected from a particular study design. The discussion and guidance provided here is of special interest for those designing occupancy studies with small sample sizes, something not uncommon in the context of ecology and conservation.
The fraction of sampling units in a landscape where a target species is present (occupancy) is an extensively used concept in ecology. Yet in many applications the species will not always be detected in a sampling unit even when present, resulting in biased estimates of occupancy. Given that sampling units are surveyed repeatedly within a relatively short timeframe, a number of similar methods have now been developed to provide unbiased occupancy estimates. However, practical guidance on the efficient design of occupancy studies has been lacking.
In this paper we comment on a number of general issues related to designing occupancy studies, including the need for clear objectives that are explicitly linked to science or management, selection of sampling units, timing of repeat surveys and allocation of survey effort. Advice on the number of repeat surveys per sampling unit is considered in terms of the variance of the occupancy estimator, for three possible study designs.
We recommend that sampling units should be surveyed a minimum of three times when detection probability is high (> 0·5 survey ⁻¹ ), unless a removal design is used.
We found that an optimal removal design will generally be the most efficient, but we suggest it may be less robust to assumption violations than a standard design.
Our results suggest that for a rare species it is more efficient to survey more sampling units less intensively, while for a common species fewer sampling units should be surveyed more intensively.
Synthesis and applications . Reliable inferences can only result from quality data. To make the best use of logistical resources, study objectives must be clearly defined; sampling units must be selected, and repeated surveys timed appropriately; and a sufficient number of repeated surveys must be conducted. Failure to do so may compromise the integrity of the study. The guidance given here on study design issues is particularly applicable to studies of species occurrence and distribution, habitat selection and modelling, metapopulation studies and monitoring programmes.
The use of presence/absence data in wildlife management and biological surveys is widespread. There is a growing interest in quantifying the sources of error associated with these data. We show that false-negative errors (failure to record a species when in fact it is present) can have a significant impact on statistical estimation of habitat models using simulated data. Then we introduce an extension of logistic modeling, the zero-inflated binomial (ZIB) model that permits the estimation of the rate of false-negative errors and the correction of estimates of the probability of occurrence for false-negative errors by using repeated. visits to the same site. Our simulations show that even relatively low rates of false negatives bias statistical estimates of habitat effects. The method with three repeated visits eliminates the bias, but estimates are relatively imprecise. Six repeated visits improve precision of estimates to levels comparable to that achieved with conventional statistics in the absence of false-negative errors In general, when error rates are less than or equal to50% greater efficiency is gained by adding more sites, whereas when error rates are >50% it is better to increase the number of repeated visits. We highlight the flexibility of the method with three case studies, clearly demonstrating the effect of false-negative errors for a range of commonly used survey methods.
The notion of being sure that you have completely eradicated an invasive species is fanciful because of imperfect detection and persistent seed banks. Eradication is commonly declared either on an ad hoc basis, on notions of seed bank longevity, or on setting arbitrary thresholds of 1% or 5% confidence that the species is not present. Rather than declaring eradication at some arbitrary level of confidence, we take an economic approach in which we stop looking when the expected costs outweigh the expected benefits. We develop theory that determines the number of years of absent surveys required to minimize the net expected cost. Given detection of a species is imperfect, the optimal stopping time is a trade-off between the cost of continued surveying and the cost of escape and damage if eradication is declared too soon. A simple rule of thumb compares well to the exact optimal solution using stochastic dynamic programming. Application of the approach to the eradication programme of Helenium amarum reveals that the actual stopping time was a precautionary one given the ranges for each parameter.
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