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.

Aerial survey estimates of polar bears and their tracks in the Chukchi Sea.

Polar bears are of international conservation concern due to climate change but are difficult to study because of low densities and an expansive, circumpolar distribution. In a collaborative U.S.-Russian effort in spring of 2016, we used aerial surveys to detect and estimate the abundance of polar bears on sea ice in the Chukchi Sea. Our surveys used a combination of thermal imagery, digital photography, and human observations. Using spatio-temporal statistical models that related bear and track densities to physiographic and biological covariates (e.g., sea ice extent, resource selection functions derived from satellite tags), we predicted abundance and spatial distribution throughout our study area. Estimates of 2016 abundance ([Formula: see text]) ranged from 3,435 (95% CI: 2,300-5,131) to 5,444 (95% CI: 3,636-8,152) depending on the proportion of bears assumed to be missed on the transect line during Russian surveys (g(0)). Our point estimates are larger than, but of similar magnitude to, a recent estimate for the period 2008-2016 ([Formula: see text]; 95% CI 1,522-5,944) derived from an integrated population model applied to a slightly smaller area. Although a number of factors (e.g., equipment issues, differing platforms, low sample sizes, size of the study area relative to sampling effort) required us to make a number of assumptions to generate estimates, it establishes a useful lower bound for abundance, and suggests high spring polar bear densities on sea ice in Russian waters south of Wrangell Island. With future improvements, we suggest that springtime aerial surveys may represent a plausible avenue for studying abundance and distribution of polar bears and their prey over large, remote areas.

Robustness of close-kin mark-recapture estimators to dispersal limitation and spatially varying sampling probabilities.

Close-kin mark-recapture (CKMR) is a method for estimating abundance and vital rates from kinship relationships observed in genetic samples. CKMR inference only requires animals to be sampled once (e.g., lethally), potentially widening the scope of population-level inference relative to traditional monitoring programs.One assumption of CKMR is that, conditional on individual covariates like age, all animals have an equal probability of being sampled. However, if genetic data are collected opportunistically (e.g., via hunters or fishers), there is potential for spatial variation in sampling probability that can bias CKMR estimators, particularly when genetically related individuals stay in close proximity.We used individual-based simulation to investigate consequences of dispersal limitation and spatially biased sampling on performance of naive (nonspatial) CKMR estimators of abundance, fecundity, and adult survival. Population dynamics approximated that of a long-lived mammal species subject to lethal sampling.Naive CKMR abundance estimators were relatively unbiased when dispersal was unconstrained (i.e., complete mixing) or when sampling was random or subject to moderate levels of spatial variation. When dispersal was limited, extreme variation in spatial sampling probabilities negatively biased abundance estimates. Reproductive schedules and survival were well estimated, except for survival when adults could emigrate out of the sampled area. Incomplete mixing was readily detected using Kolmogorov-Smirnov tests.Although CKMR appears promising for estimating abundance and vital rates with opportunistically collected genetic data, care is needed when dispersal limitation is coupled with spatially biased sampling. Fortunately, incomplete mixing is easily detected with adequate sample sizes. In principle, it is possible to devise and fit spatially explicit CKMR models to avoid bias under dispersal limitation, but development of such models necessitates additional complexity (and possibly additional data). We suggest using simulation studies to examine potential bias and precision of proposed modeling approaches prior to implementing a CKMR program.

Developing and assessing a density surface model in a Bayesian hierarchical framework with a focus on uncertainty: insights from simulations and an application to fin whales (Balaenoptera physalus).

Density surface models (DSMs) are an important tool in the conservation and management of cetaceans. Most previous applications of DSMs have adopted a two-step approach to model fitting (hereafter referred to as the Two-Stage Method), whereby detection probabilities are first estimated using distance sampling detection functions and subsequently used as an offset when fitting a density-habitat model. Although variance propagation techniques have recently become available for the Two-Stage Method, most previous applications have not propagated detection probability uncertainty into final density estimates. In this paper, we describe an alternative approach for fitting DSMs based on Bayesian hierarchical inference (hereafter referred to as the Bayesian Method), which is a natural framework for simultaneously propagating multiple sources of uncertainty into final estimates. Our framework includes (1) a mark-recapture distance sampling observation model that can accommodate two team line transect data, (2) an informed prior for the probability a group of animals is at the surface and available for detection (i.e. surface availability) (3) a density-habitat model incorporating spatial smoothers and (4) a flexible compound Poisson-gamma model for count data that incorporates overdispersion and zero-inflation. We evaluate our method and compare its performance to the Two-Stage Method with simulations and an application to line transect data of fin whales (Balaenoptera physalus) off the east coast of the USA. Simulations showed that both methods had low bias (<1.5%) and confidence interval coverage close to the nominal 95% rate when variance was propagated from the first step. Results from the fin whale analysis showed that density estimates and predicted distribution patterns were largely similar among methods; however, the coefficient of variation of the final abundance estimate more than doubled (0.14 vs 0.31) when detection variance was correctly propagated into final estimates. An analysis of the variance components demonstrated that overall detectability as well as surface availability contributed substantial amounts of variance in the final abundance estimates whereas uncertainty in mean group size contributed a negligible amount. Our method provides a Bayesian alternative to DSMs that incorporates much of the flexibility available in the Two-Stage Method. In addition, these results demonstrate the degree to which uncertainty can be underestimated if certain components of a DSM are assumed fixed.

Effects of distance on detectability of Arctic waterfowl using double-observer sampling during helicopter surveys.

Aerial survey is an important, widely employed approach for estimating free-ranging wildlife over large or inaccessible study areas. We studied how a distance covariate influenced probability of double-observer detections for birds counted during a helicopter survey in Canada's central Arctic. Two observers, one behind the other but visually obscured from each other, counted birds in an incompletely shared field of view to a distance of 200 m. Each observer assigned detections to one of five 40-m distance bins, guided by semi-transparent marks on aircraft windows. Detections were recorded with distance bin, taxonomic group, wing-flapping behavior, and group size. We compared two general model-based estimation approaches pertinent to sampling wildlife under such situations. One was based on double-observer methods without distance information, that provide sampling analogous to that required for mark-recapture (MR) estimation of detection probability, p ^ , and group abundance, G ^ , along a fixed-width strip transect. The other method incorporated double-observer MR with a categorical distance covariate (MRD). A priori, we were concerned that estimators from MR models were compromised by heterogeneity in p ^ due to un-modeled distance information; that is, more distant birds are less likely to be detected by both observers, with the predicted effect that p ^ would be biased high, and G ^ biased low. We found that, despite increased complexity, MRD models (ΔAICc range: 0-16) fit data far better than MR models (ΔAICc range: 204-258). However, contrary to expectation, the more naïve MR estimators of p ^ were biased low in all cases, but only by 2%-5% in most cases. We suspect that this apparently anomalous finding was the result of specific limitations to, and trade-offs in, visibility by observers on the survey platform used. While MR models provided acceptable point estimates of group abundance, their far higher stranded errors (0%-40%) compared to MRD estimates would compromise ability to detect temporal or spatial differences in abundance. Given improved precision of MRD models relative to MR models, and the possibility of bias when using MR methods from other survey platforms, we recommend avian ecologists use MRD protocols and estimation procedures when surveying Arctic bird populations.

Taxonomy-based hierarchical analysis of natural mortality: polar and subpolar phocid seals.

Knowledge of life-history parameters is frequently lacking in many species and populations, often because they are cryptic or logistically challenging to study, but also because life-history parameters can be difficult to estimate with adequate precision. We suggest using hierarchical Bayesian analysis (HBA) to analyze variation in life-history parameters among related species, with prior variance components representing shared taxonomy, phenotypic plasticity, and observation error. We develop such a framework to analyze U-shaped natural mortality patterns typical of mammalian life history from a variety of sparse datasets. Using 39 datasets from seals in the family Phocidae, we analyzed 16 models with different formulations for natural morality, specifically the amount of taxonomic and data-level variance components (subfamily, species, study, and dataset levels) included in mortality hazard parameters. The highest-ranked model according to DIC included subfamily-, species-, and dataset-level parameter variance components and resulted in typical U-shaped hazard functions for the 11 seal species in the study. Species with little data had survival schedules shrunken to the mean. We suggest that evolutionary and population ecologists consider employing HBA to quantify variation in life-history parameters. This approach can be useful for increasing the precision of estimates resulting from a collection of (often sparse) datasets, and for producing prior distributions for populations missing life-history data.

Using simulation to evaluate wildlife survey designs: polar bears and seals in the Chukchi Sea.

Logistically demanding and expensive wildlife surveys should ideally yield defensible estimates. Here, we show how simulation can be used to evaluate alternative survey designs for estimating wildlife abundance. Specifically, we evaluate the potential of instrument-based aerial surveys (combining infrared imagery with high-resolution digital photography to detect and identify species) for estimating abundance of polar bears and seals in the Chukchi Sea. We investigate the consequences of different levels of survey effort, flight track allocation and model configuration on bias and precision of abundance estimators. For bearded seals (0.07 animals km(-2)) and ringed seals (1.29 animals km(-2)), we find that eight flights traversing ≈7840 km are sufficient to achieve target precision levels (coefficient of variation (CV)<20%) for a 2.94×10(5) km(2) study area. For polar bears (provisionally, 0.003 animals km(-2)), 12 flights traversing ≈11 760 km resulted in CVs ranging from 28 to 35%. Estimators were relatively unbiased with similar precision over different flight track allocation strategies and estimation models, although some combinations had superior performance. These findings suggest that instrument-based aerial surveys may provide a viable means for monitoring seal and polar bear populations on the surface of the sea ice over large Arctic regions. More broadly, our simulation-based approach to evaluating survey designs can serve as a template for biologists designing their own surveys.

On Extrapolating Past the Range of Observed Data When Making Statistical Predictions in Ecology.

Ecologists are increasingly using statistical models to predict animal abundance and occurrence in unsampled locations. The reliability of such predictions depends on a number of factors, including sample size, how far prediction locations are from the observed data, and similarity of predictive covariates in locations where data are gathered to locations where predictions are desired. In this paper, we propose extending Cook's notion of an independent variable hull (IVH), developed originally for application with linear regression models, to generalized regression models as a way to help assess the potential reliability of predictions in unsampled areas. Predictions occurring inside the generalized independent variable hull (gIVH) can be regarded as interpolations, while predictions occurring outside the gIVH can be regarded as extrapolations worthy of additional investigation or skepticism. We conduct a simulation study to demonstrate the usefulness of this metric for limiting the scope of spatial inference when conducting model-based abundance estimation from survey counts. In this case, limiting inference to the gIVH substantially reduces bias, especially when survey designs are spatially imbalanced. We also demonstrate the utility of the gIVH in diagnosing problematic extrapolations when estimating the relative abundance of ribbon seals in the Bering Sea as a function of predictive covariates. We suggest that ecologists routinely use diagnostics such as the gIVH to help gauge the reliability of predictions from statistical models (such as generalized linear, generalized additive, and spatio-temporal regression models).

A hidden Markov model to identify and adjust for selection bias: an example involving mixed migration strategies.

An important assumption in observational studies is that sampled individuals are representative of some larger study population. Yet, this assumption is often unrealistic. Notable examples include online public-opinion polls, publication biases associated with statistically significant results, and in ecology, telemetry studies with significant habitat-induced probabilities of missed locations. This problem can be overcome by modeling selection probabilities simultaneously with other predictor-response relationships or by weighting observations by inverse selection probabilities. We illustrate the problem and a solution when modeling mixed migration strategies of northern white-tailed deer (Odocoileus virginianus). Captures occur on winter yards where deer migrate in response to changing environmental conditions. Yet, not all deer migrate in all years, and captures during mild years are more likely to target deer that migrate every year (i.e., obligate migrators). Characterizing deer as conditional or obligate migrators is also challenging unless deer are observed for many years and under a variety of winter conditions. We developed a hidden Markov model where the probability of capture depends on each individual's migration strategy (conditional versus obligate migrator), a partially latent variable that depends on winter severity in the year of capture. In a 15-year study, involving 168 white-tailed deer, the estimated probability of migrating for conditional migrators increased nonlinearly with an index of winter severity. We estimated a higher proportion of obligates in the study cohort than in the population, except during a span of 3 years surrounding back-to-back severe winters. These results support the hypothesis that selection biases occur as a result of capturing deer on winter yards, with the magnitude of bias depending on the severity of winter weather. Hidden Markov models offer an attractive framework for addressing selection biases due to their ability to incorporate latent variables and model direct and indirect links between state variables and capture probabilities.

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).

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").

A hierarchical modeling framework for multiple observer transect surveys.

Ecologists often use multiple observer transect surveys to census animal populations. In addition to animal counts, these surveys produce sequences of detections and non-detections for each observer. When combined with additional data (i.e. covariates such as distance from the transect line), these sequences provide the additional information to estimate absolute abundance when detectability on the transect line is less than one. Although existing analysis approaches for such data have proven extremely useful, they have some limitations. For instance, it is difficult to extrapolate from observed areas to unobserved areas unless a rigorous sampling design is adhered to; it is also difficult to share information across spatial and temporal domains or to accommodate habitat-abundance relationships. In this paper, we introduce a hierarchical modeling framework for multiple observer line transects that removes these limitations. In particular, abundance intensities can be modeled as a function of habitat covariates, making it easier to extrapolate to unsampled areas. Our approach relies on a complete data representation of the state space, where unobserved animals and their covariates are modeled using a reversible jump Markov chain Monte Carlo algorithm. Observer detections are modeled via a bivariate normal distribution on the probit scale, with dependence induced by a distance-dependent correlation parameter. We illustrate performance of our approach with simulated data and on a known population of golf tees. In both cases, we show that our hierarchical modeling approach yields accurate inference about abundance and related parameters. In addition, we obtain accurate inference about population-level covariates (e.g. group size). We recommend that ecologists consider using hierarchical models when analyzing multiple-observer transect data, especially when it is difficult to rigorously follow pre-specified sampling designs. We provide a new R package, hierarchicalDS, to facilitate the building and fitting of these models.

Integrated population modeling of black bears in Minnesota: implications for monitoring and management.

BACKGROUND: Wildlife populations are difficult to monitor directly because of costs and logistical challenges associated with collecting informative abundance data from live animals. By contrast, data on harvested individuals (e.g., age and sex) are often readily available. Increasingly, integrated population models are used for natural resource management because they synthesize various relevant data into a single analysis. METHODOLOGY/PRINCIPAL FINDINGS: We investigated the performance of integrated population models applied to black bears (Ursus americanus) in Minnesota, USA. Models were constructed using sex-specific age-at-harvest matrices (1980-2008), data on hunting effort and natural food supplies (which affects hunting success), and statewide mark-recapture estimates of abundance (1991, 1997, 2002). We compared this approach to Downing reconstruction, a commonly used population monitoring method that utilizes only age-at-harvest data. We first conducted a large-scale simulation study, in which our integrated models provided more accurate estimates of population trends than did Downing reconstruction. Estimates of trends were robust to various forms of model misspecification, including incorrectly specified cub and yearling survival parameters, age-related reporting biases in harvest data, and unmodeled temporal variability in survival and harvest rates. When applied to actual data on Minnesota black bears, the model predicted that harvest rates were negatively correlated with food availability and positively correlated with hunting effort, consistent with independent telemetry data. With no direct data on fertility, the model also correctly predicted 2-point cycles in cub production. Model-derived estimates of abundance for the most recent years provided a reasonable match to an empirical population estimate obtained after modeling efforts were completed. CONCLUSIONS/SIGNIFICANCE: Integrated population modeling provided a reasonable framework for synthesizing age-at-harvest data, periodic large-scale abundance estimates, and measured covariates thought to affect harvest rates of black bears in Minnesota. Collection and analysis of these data appear to form the basis of a robust and viable population monitoring program.

Bayesian analysis of wildlife age-at-harvest data.

SUMMARY: State and federal natural resource management agencies often collect age-structured harvest data. These data represent finite realizations of stochastic demographic and sampling processes and have long been used by biologists to infer population trends. However, different sources of data have been combined in ad hoc ways and these methods usually failed to incorporate sampling error. In this article, we propose a "hidden process" (or state-space) model for estimating abundance, survival, recovery rate, and recruitment from age-at-harvest data that incorporate both demographic and sampling stochasticity. To this end, a likelihood for age-at-harvest data is developed by embedding a population dynamics model within a model for the sampling process. Under this framework, the identification of abundance parameters can be achieved by conducting a joint analysis with an auxiliary data set. We illustrate this approach by conducting a Bayesian analysis of age-at-harvest and mark-recovery data from black bears (Ursus americanus) in Pennsylvania. Using a set of reasonable prior distributions, we demonstrate a substantial increase in precision when posterior summaries of abundance are compared to a bias-corrected Lincoln-Petersen estimator. Because demographic processes link consecutive abundance estimates, we also obtain a more realistic biological picture of annual changes in abundance. Because age-at-harvest data are often readily obtained, we argue that this type of analysis provides a valuable strategy for wildlife population monitoring.

Adjusting age and stage distributions for misclassification errors.

Ecologists often use samples from the age or stage structure of a population to make inferences about population-level processes and to parameterize matrix models. Typically, researchers make a simplifying assumption that age and stage classes are determined without error, when in fact some level of misclassification often can be expected. If unaccounted for, misclassification will lead to overly optimistic levels of precision and can cause biased estimates of age or stage structure. Although several studies have used information from known-age individuals to quantify errors in age or stage distribution, the problem of estimating the age or stage structure in face of such errors has received comparably little attention. In this paper, we describe a general statistical framework for estimating the true stage distribution of a sample when misclassification rates can be estimated. The estimation process requires auxiliary information on misclassification rates, such as data from individuals of known age. We analyze age-structured harvest records from black bears in Pennsylvania to illustrate how incorporating misclassification errors leads to changes in point estimates and provides a measure of precision.

Estimating the abundance of mouse populations of known size: promises and pitfalls of new methods.

Knowledge of animal abundance is fundamental to many ecological studies. Frequently, researchers cannot determine true abundance, and so must estimate it using a method such as mark-recapture or distance sampling. Recent advances in abundance estimation allow one to model heterogeneity with individual covariates or mixture distributions and to derive multimodel abundance estimators that explicitly address uncertainty about which model parameterization best represents truth. Further, it is possible to borrow information on detection probability across several populations when data are sparse. While promising, these methods have not been evaluated using mark-recapture data from populations of known abundance, and thus far have largely been overlooked by ecologists. In this paper, we explored the utility of newly developed mark-recapture methods for estimating the abundance of 12 captive populations of wild house mice (Mus musculus). We found that mark-recapture methods employing individual covariates yielded satisfactory abundance estimates for most populations. In contrast, model sets with heterogeneity formulations consisting solely of mixture distributions did not perform well for several of the populations. We show through simulation that a higher number of trapping occasions would have been necessary to achieve good estimator performance in this case. Finally, we show that simultaneous analysis of data from low abundance populations can yield viable abundance estimates.

Combining multistate capture-recapture data with tag recoveries to estimate demographic parameters.

Matrix population models that allow an animal to occupy more than one state over time are important tools for population and evolutionary ecologists. Definition of state can vary, including location for metapopulation models and breeding state for life history models. For populations whose members can be marked and subsequently reencountered, multistate mark-recapture models are available to estimate the survival and transition probabilities needed to construct population models. Multistate models have proved extremely useful in this context, but they often require a substantial amount of data and restrict estimation of transition probabilities to those areas or states subjected to formal sampling effort. At the same time, for many species, there are considerable tag recovery data provided by the public that could be modeled in order to increase precision and to extend inference to a greater number of areas or states. Here we present a statistical model for combining multistate capture-recapture data (e.g., from a breeding ground study) with multistate tag recovery data (e.g., from wintering grounds). We use this method to analyze data from a study of Canada Geese (Branta canadensis) in the Atlantic Flyway of North America. Our analysis produced marginal improvement in precision, due to relatively few recoveries, but we demonstrate how precision could be further improved with increases in the probability that a retrieved tag is reported.

A general model for the analysis of mark-resight, mark-recapture, and band-recovery data under tag loss.

Estimates of waterfowl demographic parameters often come from resighting studies where birds fit with individually identifiable neck collars are resighted at a distance. Concerns have been raised about the effects of collar loss on parameter estimates, and the reliability of extrapolating from collared individuals to the population. Models previously proposed to account for collar loss do not allow survival or harvest parameters to depend on neck collar presence or absence. Also, few models have incorporated recent advances in mark-recapture theory that allow for multiple states or auxiliary encounters such as band recoveries. We propose a multistate model for tag loss in which the presence or absence of a collar is considered as a state variable. In this framework, demographic parameters are corrected for tag loss and questions related to collar effects on survival and recovery rates can be addressed. Encounters of individuals between closed sampling periods also can be incorporated in the analysis. We discuss data requirements for answering questions related to tag loss and sampling designs that lend themselves to this purpose. We illustrate the application of our model using a study of lesser snow geese (Chen caerulescens caerulescens).