A multistate Langevin diffusion for inferring behavior-specific habitat selection and utilization distributions.

The identification of important habitat and the behavior(s) associated with it is critical to conservation and place-based management decisions. Behavior also links life-history requirements and habitat use, which are key to understanding why animals use certain habitats. Animal population studies often use tracking data to quantify space use and habitat selection, but they typically either ignore movement behavior (e.g., foraging, migrating, nesting) or adopt a two-stage approach that can induce bias and fail to propagate uncertainty. We develop a habitat-driven Langevin diffusion for animals that exhibit distinct movement behavior states, thereby providing a novel single-stage statistical method for inferring behavior-specific habitat selection and utilization distributions in continuous time. Practitioners can customize, fit, assess, and simulate our integrated model using the provided R package. Simulation experiments demonstrated that the model worked well under a range of sampling scenarios as long as observations were of sufficient temporal resolution. Our simulations also demonstrated the importance of accounting for different behaviors and the misleading inferences that can result when these are ignored. We provide case studies using plains zebra (Equus quagga) and Steller sea lion (Eumetopias jubatus) telemetry data. In the zebra example, our model identified distinct "encamped" and "exploratory" states, where the encamped state was characterized by strong selection for grassland and avoidance of other vegetation types, which may represent selection for foraging resources. In the sea lion example, our model identified distinct movement behavior modes typically associated with this marine central-place forager and, unlike previous analyses, found foraging-type movements to be associated with steeper offshore slopes characteristic of the continental shelf, submarine canyons, and seamounts that are believed to enhance prey concentrations. This is the first single-stage approach for inferring behavior-specific habitat selection and utilization distributions from tracking data that can be readily implemented with user-friendly software. As certain behaviors are often more relevant to specific conservation or management objectives, practitioners can use our model to help inform the identification and prioritization of important habitats. Moreover, by linking individual-level movement behaviors to population-level spatial processes, the multistate Langevin diffusion can advance inferences at the intersection of population, movement, and landscape ecology.

Integrated animal movement and spatial capture-recapture models: Simulation, implementation, and inference.

Over the last decade, spatial capture-recapture (SCR) models have become widespread for estimating demographic parameters in ecological studies. However, the underlying assumptions about animal movement and space use are often not realistic. This is a missed opportunity because interesting ecological questions related to animal space use, habitat selection, and behavior cannot be addressed with most SCR models, despite the fact that the data collected in SCR studies - individual animals observed at specific locations and times - can provide a rich source of information about these processes and how they relate to demographic rates. We developed SCR models that integrated more complex movement processes that are typically inferred from telemetry data, including a simple random walk, correlated random walk (i.e., short-term directional persistence), and habitat-driven Langevin diffusion. We demonstrated how to formulate, simulate from, and fit these models with standard SCR data using data-augmented Bayesian analysis methods. We evaluated their performance through a simulation study, in which we varied the detection, movement, and resource selection parameters. We also examined different numbers of sampling occasions and assessed performance gains when including auxiliary location data collected from telemetered individuals. Across all scenarios, the integrated SCR movement models performed well in terms of abundance, detection, and movement parameter estimation. We found little difference in bias for the simple random walk model when reducing the number of sampling occasions from T = 25 to T = 15. We found some bias in movement parameter estimates under several of the correlated random walk scenarios, but incorporating auxiliary location data improved parameter estimates and significantly improved mixing during model fitting. The Langevin movement model was able to recover resource selection parameters from standard SCR data, which is particularly appealing because it explicitly links the individual-level movement process with habitat selection and population density. We focused on closed population models, but the movement models developed here can be extended to open SCR models. The movement process models could also be easily extended to accommodate additional "building blocks" of random walks, such as central tendency (e.g., territoriality) or multiple movement behavior states, thereby providing a flexible and coherent framework for linking animal movement behavior to population dynamics, density, and distribution.

An integrated path for spatial capture-recapture and animal movement modeling.

Ecologists and conservation biologists increasingly rely on spatial capture-recapture (SCR) and movement modeling to study animal populations. Historically, SCR has focused on population-level processes (e.g., vital rates, abundance, density, and distribution), whereas animal movement modeling has focused on the behavior of individuals (e.g., activity budgets, resource selection, migration). Even though animal movement is clearly a driver of population-level patterns and dynamics, technical and conceptual developments to date have not forged a firm link between the two fields. Instead, movement modeling has typically focused on the individual level without providing a coherent scaling from individual- to population-level processes, whereas SCR has typically focused on the population level while greatly simplifying the movement processes that give rise to the observations underlying these models. In our view, the integration of SCR and animal movement modeling has tremendous potential for allowing ecologists to scale up from individuals to populations and advancing the types of inferences that can be made at the intersection of population, movement, and landscape ecology. Properly accounting for complex animal movement processes can also potentially reduce bias in estimators of population-level parameters, thereby improving inferences that are critical for species conservation and management. This introductory article to the Special Feature reviews recent advances in SCR and animal movement modeling, establishes a common notation, highlights potential advantages of linking individual-level (Lagrangian) movements to population-level (Eulerian) processes, and outlines a general conceptual framework for the integration of movement and SCR models. We then identify important avenues for future research, including key challenges and potential pitfalls in the developments and applications that lie ahead.

Uncovering ecological state dynamics with hidden Markov models.

Ecological systems can often be characterised by changes among a finite set of underlying states pertaining to individuals, populations, communities or entire ecosystems through time. Owing to the inherent difficulty of empirical field studies, ecological state dynamics operating at any level of this hierarchy can often be unobservable or 'hidden'. Ecologists must therefore often contend with incomplete or indirect observations that are somehow related to these underlying processes. By formally disentangling state and observation processes based on simple yet powerful mathematical properties that can be used to describe many ecological phenomena, hidden Markov models (HMMs) can facilitate inferences about complex system state dynamics that might otherwise be intractable. However, HMMs have only recently begun to gain traction within the broader ecological community. We provide a gentle introduction to HMMs, establish some common terminology, review the immense scope of HMMs for applied ecological research and provide a tutorial on implementation and interpretation. By illustrating how practitioners can use a simple conceptual template to customise HMMs for their specific systems of interest, revealing methodological links between existing applications, and highlighting some practical considerations and limitations of these approaches, our goal is to help establish HMMs as a fundamental inferential tool for ecologists.

Spatial capture-recapture with multiple noninvasive marks: An application to camera-trapping data of the European wildcat (Felis silvestris) using R package multimark.

In Switzerland, the European wildcat (Felis silvestris), a native felid, is protected by national law. In recent decades, the wildcat has slowly returned to much of its original range and may have even expanded into new areas that were not known to be occupied before. For the implementation of efficient conservation actions, reliable information about the status and trend of population size and density is crucial. But so far, only one reliable estimate of density in Switzerland was produced in the northern Swiss Jura Mountains. Wildcats are relatively rare and elusive, but camera trapping has proven to be an effective method for monitoring felids. We developed and tested a monitoring protocol using camera trapping in the northern Jura Mountains (cantons of Bern and Jura) in an area of 100 km2. During 60 days, we obtained 105 pictures of phenotypical wildcats of which 98 were suitable for individual identification. We identified 13 individuals from both sides and, additionally, 5 single right-sided flanks and 3 single left-sided flanks that could not be matched to unique individuals. We analyzed the camera-trap data using the R package multimark, which has been extended to include a novel spatial capture-recapture model for encounter histories that include multiple "noninvasive" marks, such as bilaterally asymmetrical left- and right-sided flanks, that can be difficult (or impossible) to reliably match to individuals. Here, we present this model in detail for the first time. Based on a "semi-complete" data likelihood, the model is less computationally demanding than Bayesian alternatives that rely on a data-augmented complete data likelihood. The spatially explicit capture-recapture model estimated a wildcat density (95% credible interval) of 26 (17-36) per 100 km2 suitable habitat. Our integrated model produced higher abundance and density estimates with improved precision compared to single-sided analyses, suggesting spatially explicit capture-recapture methods with multiple "noninvasive" marks can improve our ability to monitor wildcat population status.

A paradox of local abundance amidst regional rarity: the value of montane refugia for Persian leopard conservation.

The population densities of leopards vary widely across their global range, influenced by prey availability, intraguild competition and human persecution. In Asia, particularly the Middle East and the Caucasus, they generally occur at the lower extreme of densities recorded for the species. Reliable estimates of population density are important for understanding their ecology and planning their conservation. We used a photographic spatial capture-recapture (SCR) methodology incorporating animal movement to estimate density for the endangered Persian leopard Panthera pardus saxicolor in three montane national parks, northeastern Iran. We combined encounter history data arising from images of bilaterally asymmetrical left- and right-sided pelage patterns using a Bayesian spatial partial identity model accommodating multiple "non-invasive" marks. We also investigated the effect of camera trap placement on detection probability. Surprisingly, considering the subspecies' reported low abundance and density based on previous studies, we found relatively high population densities in the three national parks, varying between 3.10 ± SD 1.84 and 8.86 ± SD 3.60 individuals/100 km2. The number of leopards detected in Tandoureh National Park (30 individuals) was larger than estimated during comparable surveys at any other site in Iran, or indeed globally. Capture and recapture probabilities were higher for camera traps placed near water resources compared with those placed on trails. Our results show the benefits of protecting even relatively small mountainous areas, which accommodated a high density of leopards and provided refugia in a landscape with substantial human activity.

Improved methods for estimating abundance and related demographic parameters from mark-resight data.

Over the past decade, there has been much methodological development for the estimation of abundance and related demographic parameters using mark-resight data. Often viewed as a less-invasive and less-expensive alternative to conventional mark recapture, mark-resight methods jointly model marked individual encounters and counts of unmarked individuals, and recent extensions accommodate common challenges associated with imperfect detection. When these challenges include both individual detection heterogeneity and an unknown marked sample size, we demonstrate several deficiencies associated with the most widely used mark-resight models currently implemented in the popular capture-recapture freeware Program MARK. We propose a composite likelihood solution based on a zero-inflated Poisson log-normal model and find the performance of this new estimator to be superior in terms of bias and confidence interval coverage. Under Pollock's robust design, we also extend the models to accommodate individual-level random effects across sampling occasions as a potentially more realistic alternative to models that assume independence. As a motivating example, we revisit a previous analysis of mark-resight data for the New Zealand Robin (Petroica australis) and compare inferences from the proposed estimators. For the all-too-common situation where encounter rates are low, individual detection heterogeneity is non-negligible, and the number of marked individuals is unknown, we recommend practitioners use the zero-inflated Poisson log-normal mark-resight estimator as now implemented in Program MARK.

multimark: an R package for analysis of capture-recapture data consisting of multiple "noninvasive" marks.

I describe an open-source R package, multimark, for estimation of survival and abundance from capture-mark-recapture data consisting of multiple "noninvasive" marks. Noninvasive marks include natural pelt or skin patterns, scars, and genetic markers that enable individual identification in lieu of physical capture. multimark provides a means for combining and jointly analyzing encounter histories from multiple noninvasive sources that otherwise cannot be reliably matched (e.g., left- and right-sided photographs of bilaterally asymmetrical individuals). The package is currently capable of fitting open population Cormack-Jolly-Seber (CJS) and closed population abundance models with up to two mark types using Bayesian Markov chain Monte Carlo (MCMC) methods. multimark can also be used for Bayesian analyses of conventional capture-recapture data consisting of a single-mark type. Some package features include (1) general model specification using formulas already familiar to most R users, (2) ability to include temporal, behavioral, age, cohort, and individual heterogeneity effects in detection and survival probabilities, (3) improved MCMC algorithm that is computationally faster and more efficient than previously proposed methods, (4) Bayesian multimodel inference using reversible jump MCMC, and (5) data simulation capabilities for power analyses and assessing model performance. I demonstrate use of multimark using left- and right-sided encounter histories for bobcats (Lynx rufus) collected from remote single-camera stations in southern California. In this example, there is evidence of a behavioral effect (i.e., trap "happy" response) that is otherwise indiscernible using conventional single-sided analyses. The package will be most useful to ecologists seeking stronger inferences by combining different sources of mark-recapture data that are difficult (or impossible) to reliably reconcile, particularly with the sparse datasets typical of rare or elusive species for which noninvasive sampling techniques are most commonly employed. Addressing deficiencies in currently available software, multimark also provides a user-friendly interface for performing Bayesian multimodel inference using capture-recapture data consisting of a single conventional mark or multiple noninvasive marks.

Mark-recapture and mark-resight methods for estimating abundance with remote cameras: a carnivore case study.

Abundance estimation of carnivore populations is difficult and has prompted the use of non-invasive detection methods, such as remotely-triggered cameras, to collect data. To analyze photo data, studies focusing on carnivores with unique pelage patterns have utilized a mark-recapture framework and studies of carnivores without unique pelage patterns have used a mark-resight framework. We compared mark-resight and mark-recapture estimation methods to estimate bobcat (Lynx rufus) population sizes, which motivated the development of a new "hybrid" mark-resight model as an alternative to traditional methods. We deployed a sampling grid of 30 cameras throughout the urban southern California study area. Additionally, we physically captured and marked a subset of the bobcat population with GPS telemetry collars. Since we could identify individual bobcats with photos of unique pelage patterns and a subset of the population was physically marked, we were able to use traditional mark-recapture and mark-resight methods, as well as the new "hybrid" mark-resight model we developed to estimate bobcat abundance. We recorded 109 bobcat photos during 4,669 camera nights and physically marked 27 bobcats with GPS telemetry collars. Abundance estimates produced by the traditional mark-recapture, traditional mark-resight, and "hybrid" mark-resight methods were similar, however precision differed depending on the models used. Traditional mark-recapture and mark-resight estimates were relatively imprecise with percent confidence interval lengths exceeding 100% of point estimates. Hybrid mark-resight models produced better precision with percent confidence intervals not exceeding 57%. The increased precision of the hybrid mark-resight method stems from utilizing the complete encounter histories of physically marked individuals (including those never detected by a camera trap) and the encounter histories of naturally marked individuals detected at camera traps. This new estimator may be particularly useful for estimating abundance of uniquely identifiable species that are difficult to sample using camera traps alone.

When to be discrete: the importance of time formulation in understanding animal movement.

Animal movement is essential to our understanding of population dynamics, animal behavior, and the impacts of global change. Coupled with high-resolution biotelemetry data, exciting new inferences about animal movement have been facilitated by various specifications of contemporary models. These approaches differ, but most share common themes. One key distinction is whether the underlying movement process is conceptualized in discrete or continuous time. This is perhaps the greatest source of confusion among practitioners, both in terms of implementation and biological interpretation. In general, animal movement occurs in continuous time but we observe it at fixed discrete-time intervals. Thus, continuous time is conceptually and theoretically appealing, but in practice it is perhaps more intuitive to interpret movement in discrete intervals. With an emphasis on state-space models, we explore the differences and similarities between continuous and discrete versions of mechanistic movement models, establish some common terminology, and indicate under which circumstances one form might be preferred over another. Counter to the overly simplistic view that discrete- and continuous-time conceptualizations are merely different means to the same end, we present novel mathematical results revealing hitherto unappreciated consequences of model formulation on inferences about animal movement. Notably, the speed and direction of movement are intrinsically linked in current continuous-time random walk formulations, and this can have important implications when interpreting animal behavior. We illustrate these concepts in the context of state-space models with multiple movement behavior states using northern fur seal (Callorhinus ursinus) biotelemetry data.

Integrated modeling of bilateral photo-identification data in mark-recapture analyses.

When natural marks provide sufficient resolution to identify individual animals, noninvasive sampling using cameras has a number of distinct advantages relative to "traditional" mark-recapture methods. However, analyses from photo-identification records often pose additional challenges. For example, it is often unclear how to link left- and right-side photos to the same individual, and previous studies have primarily used data from just one side for statistical inference. Here we describe how a recently developed statistical method can be adapted for integrated mark-recapture analyses using bilateral photo-identification records. The approach works by assuming that the true encounter history for each animal is a latent (unobserved) realization from a multinomial distribution. Based on the type of photo encounter (e.g., right, left, or both sides), the recorded (observed) encounter histories can only arise from certain combinations of these latent histories. In this manner, the approach properly accounts for uncertainty about the true number of distinct animals observed in the study. Using a Markov chain Monte Carlo sampling procedure, we conduct a small simulation study to show that this approach has reasonable properties and outperforms other methods. We further illustrate our approach by estimating population size from bobcat photo-identification records. Although motivated by bilateral photo-identification records, we note that the proposed methodology can be used to combine and jointly analyze other types of mark-recapture data (e.g., photo and DNA records).

A spatial mark--resight model augmented with telemetry data.

Abundance and population density are fundamental pieces of information for population ecology and species conservation, but they are difficult to estimate for rare and elusive species. Mark--resight models are popular for estimating population abundance because they are less invasive and expensive than traditional mark-recapture. However, density estimation using mark-resight is difficult because the area sampled must be explicitly defined, historically using ad hoc approaches. We developed a spatial mark--resight model for estimating population density that combines spatial resighting data and telemetry data. Incorporating telemetry data allows us to inform model parameters related to movement and individual location. Our model also allows <100% individual identification of marked individuals. We implemented the model in a Bayesian framework, using a custom-made Metropolis-within-Gibbs Markov chain Monte Carlo algorithm. As an example, we applied this model to a mark--resight study of raccoons (Procyon lotor) on South Core Banks, a barrier island in Cape Lookout National Seashore, North Carolina, USA. We estimated a population of 186.71 +/- 14.81 individuals, which translated to a density of 8.29 +/- 0.66 individuals/km2 (mean +/- SD). The model presented here will have widespread utility in future applications, especially for species that are not naturally marked.

Accommodating species identification errors in transect surveys.

Ecologists often use transect surveys to estimate the density and abundance of animal populations. Errors in species classification are often evident in such surveys, yet few statistical methods exist to properly account for them. In this paper, we examine biases that result from species misidentification when ignored, and we develop statistical models to provide unbiased estimates of density in the face of such errors. Our approach treats true species identity as a latent variable and requires auxiliary information on the misclassification process (such as informative priors, experiments using known species, or a double-observer protocol). We illustrate our approach with simulated census data and with double-observer survey data for ice-associated seals in the Bering Sea. For the seal analysis, we integrated misclassification into a model-based framework for distance-sampling data. The simulated data analysis demonstrated reliable estimation of animal density when there are experimental data to inform misclassification rates; double-observer protocols provided robust inference when there were "unknown" species observations but no outright misclassification, or when misclassification probabilities were symmetric and a symmetry constraint was imposed during estimation. Under our modeling framework, we obtained reasonable apparent densities of seal species even under considerable imprecision in species identification. We obtained more reliable inferences when modeling variation in density among transects. We argue that ecologists should often use spatially explicit models to account for differences in species distributions when trying to account for species misidentification. Our results support using double-observer sampling protocols that guard against species misclassification (i.e., by recording uncertain observations as "unknown").

Experimental investigation of false positive errors in auditory species occurrence surveys.

False positive errors are a significant component of many ecological data sets, which in combination with false negative errors, can lead to severe biases in conclusions about ecological systems. We present results of a field experiment where observers recorded observations for known combinations of electronically broadcast calling anurans under conditions mimicking field surveys to determine species occurrence. Our objectives were to characterize false positive error probabilities for auditory methods based on a large number of observers, to determine if targeted instruction could be used to reduce false positive error rates, and to establish useful predictors of among-observer and among-species differences in error rates. We recruited 31 observers, ranging in abilities from novice to expert, who recorded detections for 12 species during 180 calling trials (66,960 total observations). All observers made multiple false positive errors, and on average 8.1% of recorded detections in the experiment were false positive errors. Additional instruction had only minor effects on error rates. After instruction, false positive error probabilities decreased by 16% for treatment individuals compared to controls with broad confidence interval overlap of 0 (95% CI:--46 to 30%). This coincided with an increase in false negative errors due to the treatment (26%;--3 to 61%). Differences among observers in false positive and in false negative error rates were best predicted by scores from an online test and a self-assessment of observer ability completed prior to the field experiment. In contrast, years of experience conducting call surveys was a weak predictor of error rates. False positive errors were also more common for species that were played more frequently but were not related to the dominant spectral frequency of the call. Our results corroborate other work that demonstrates false positives are a significant component of species occurrence data collected by auditory methods. Instructing observers to only report detections they are completely certain are correct is not sufficient to eliminate errors. As a result, analytical methods that account for false positive errors will be needed, and independent testing of observer ability is a useful predictor for among-observer variation in observation error rates.

Improving occupancy estimation when two types of observational error occur: non-detection and species misidentification.

Efforts to draw inferences about species occurrence frequently account for false negatives, the common situation when individuals of a species are not detected even when a site is occupied. However, recent studies suggest the need to also deal with false positives, which occur when species are misidentified so that a species is recorded as detected when a site is unoccupied. Bias in estimators of occupancy, colonization, and extinction can be severe when false positives occur. Accordingly, we propose models that simultaneously account for both types of error. Our approach can be used to improve estimates of occupancy for study designs where a subset of detections is of a type or method for which false positives can be assumed to not occur. We illustrate properties of the estimators with simulations and data for three species of frogs. We show that models that account for possible misidentification have greater support (lower AIC for two species) and can yield substantially different occupancy estimates than those that do not. When the potential for misidentification exists, researchers should consider analytical techniques that can account for this source of error, such as those presented here.

Unmodeled observation error induces bias when inferring patterns and dynamics of species occurrence via aural detections.

The recent surge in the development and application of species occurrence models has been associated with an acknowledgment among ecologists that species are detected imperfectly due to observation error. Standard models now allow unbiased estimation of occupancy probability when false negative detections occur, but this is conditional on no false positive detections and sufficient incorporation of explanatory variables for the false negative detection process. These assumptions are likely reasonable in many circumstances, but there is mounting evidence that false positive errors and detection probability heterogeneity may be much more prevalent in studies relying on auditory cues for species detection (e.g., songbird or calling amphibian surveys). We used field survey data from a simulated calling anuran system of known occupancy state to investigate the biases induced by these errors in dynamic models of species occurrence. Despite the participation of expert observers in simplified field conditions, both false positive errors and site detection probability heterogeneity were extensive for most species in the survey. We found that even low levels of false positive errors, constituting as little as 1% of all detections, can cause severe overestimation of site occupancy, colonization, and local extinction probabilities. Further, unmodeled detection probability heterogeneity induced substantial underestimation of occupancy and overestimation of colonization and local extinction probabilities. Completely spurious relationships between species occurrence and explanatory variables were also found. Such misleading inferences would likely have deleterious implications for conservation and management programs. We contend that all forms of observation error, including false positive errors and heterogeneous detection probabilities, must be incorporated into the estimation framework to facilitate reliable inferences about occupancy and its associated vital rate parameters.

Seeking a second opinion: uncertainty in disease ecology.

Analytical methods accounting for imperfect detection are often used to facilitate reliable inference in population and community ecology. We contend that similar approaches are needed in disease ecology because these complicated systems are inherently difficult to observe without error. For example, wildlife disease studies often designate individuals, populations, or spatial units to states (e.g., susceptible, infected, post-infected), but the uncertainty associated with these state assignments remains largely ignored or unaccounted for. We demonstrate how recent developments incorporating observation error through repeated sampling extend quite naturally to hierarchical spatial models of disease effects, prevalence, and dynamics in natural systems. A highly pathogenic strain of avian influenza virus in migratory waterfowl and a pathogenic fungus recently implicated in the global loss of amphibian biodiversity are used as motivating examples. Both show that relatively simple modifications to study designs can greatly improve our understanding of complex spatio-temporal disease dynamics by rigorously accounting for uncertainty at each level of the hierarchy.

A less field-intensive robust design for estimating demographic parameters with mark-resight data.

The robust design has become popular among animal ecologists as a means for estimating population abundance and related demographic parameters with mark-recapture data. However, two drawbacks of traditional mark-recapture are financial cost and repeated disturbance to animals. Mark-resight methodology may in many circumstances be a less expensive and less invasive alternative to mark-recapture, but the models developed to date for these data have overwhelmingly concentrated only on the estimation of abundance. Here we introduce a mark-resight model analogous to that used in mark-recapture for the simultaneous estimation of abundance, apparent survival, and transition probabilities between observable and unobservable states. The model may be implemented using standard statistical computing software, but it has also been incorporated into the freeware package Program MARK. We illustrate the use of our model with mainland New Zealand Robin (Petroica australis) data collected to ascertain whether this methodology may be a reliable alternative for monitoring endangered populations of a closely related species inhabiting the Chatham Islands. We found this method to be a viable alternative to traditional mark-recapture when cost or disturbance to species is of particular concern in long-term population monitoring programs.