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Checking that models adequately represent data is an essential component of applied statistical inference. Ecologists increasingly use hierarchical Bayesian statistical models in their research. The appeal of this modeling paradigm is undeniable, as researchers can build and fit models that embody complex ecological processes while simultaneously accounting for observation error. However, ecologists tend to be less focused on checking model assumptions and assessing potential lack of fit when applying Bayesian methods than when applying more traditional modes of inference such as maximum likelihood. There are also multiple ways of assessing the fit of Bayesian models, each of which has strengths and weaknesses. For instance, Bayesian P values are relatively easy to compute, but are well known to be conservative, producing P values biased toward 0.5. Alternatively, lesser known approaches to model checking, such as prior predictive checks, cross-validation probability integral transforms, and pivot discrepancy measures may produce more accurate characterizations of goodness-of-fit but are not as well known to ecologists. In addition, a suite of visual and targeted diagnostics can be used to examine violations of different model assumptions and lack of fit at different levels of the modeling hierarchy, and to check for residual temporal or spatial autocorrelation. In this review, we synthesize existing literature to guide ecologists through the many available options for Bayesian model checking. We illustrate methods and procedures with several ecological case studies including (1) analysis of simulated spatiotemporal count data, (2) N-mixture models for estimating abundance of sea otters from an aircraft, and (3) hidden Markov modeling to describe attendance patterns of California sea lion mothers on a rookery. We find that commonly used procedures based on posterior predictive P values detect extreme model inadequacy, but often do not detect more subtle cases of lack of fit. Tests based on cross-validation and pivot discrepancy measures (including the \"sampled predictive P value\") appear to be better suited to model checking and to have better overall statistical performance. We conclude that model checking is necessary to ensure that scientific inference is well founded. As an essential component of scientific discovery, it should accompany most Bayesian analyses presented in the literature.

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.

We propose a continuous-time version of the correlated random walk model for animal telemetry data. The continuous-time formulation allows data that have been nonuniformly collected over time to be modeled without subsampling, interpolation, or aggregation to obtain a set of locations uniformly spaced in time. The model is derived from a continuous-time Ornstein-Uhlenbeck velocity process that is integrated to form a location process. The continuous-time model was placed into a state—space framework to allow parameter estimation and location predictions from observed animal locations. Two previously unpublished marine mammal telemetry data sets were analyzed to illustrate use of the model, by-products available from the analysis, and different modifications which are possible. A harbor seal data set was analyzed with a model that incorporates the proportion of each hour spent on land. Also, a northern fur seal pup data set was analyzed with a random drift component to account for directed travel and ocean currents.

Since its development, occupancy modeling has become a popular and useful tool for ecologists wishing to learn about the dynamics of species occurrence over time and space. Such models require presence-absence data to be collected at spatially indexed survey units. However, only recently have researchers recognized the need to correct for spatially induced overdisperison by explicitly accounting for spatial autocorrelation in occupancy probability. Previous efforts to incorporate such autocorrelation have largely focused on logit-normal formulations for occupancy, with spatial autocorrelation induced by a random effect within a hierarchical modeling framework. Although useful, computational time generally limits such an approach to relatively small data sets, and there are often problems with algorithm instability, yielding unsatisfactory results. Further, recent research has revealed a hidden form of multicollinearity in such applications, which may lead to parameter bias if not explicitly addressed. Combining several techniques, we present a unifying hierarchical spatial occupancy model specification that is particularly effective over large spatial extents. This approach employs a probit mixture framework for occupancy and can easily accommodate a reduced-dimensional spatial process to resolve issues with multicollinearity and spatial confounding while improving algorithm convergence. Using open-source software, we demonstrate this new model specification using a case study involving occupancy of caribou ( Rangifer tarandus ) over a set of 1080 survey units spanning a large contiguous region (108 000 km 2 ) in northern Ontario, Canada. Overall, the combination of a more efficient specification and open-source software allows for a facile and stable implementation of spatial occupancy models for large data sets.

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).

The dynamic, multi‐season occupancy model framework has become a popular tool for modeling open populations with occupancies that change over time through local colonizations and extinctions. However, few versions of the model relate these probabilities to the occupancies of neighboring sites or patches. We present a modeling framework that incorporates this information and is capable of describing a wide variety of spatiotemporal colonization and extinction processes. A key feature of the model is that it is based on a simple set of small‐scale rules describing how the process evolves. The result is a dynamic process that can account for complicated large‐scale features. In our model, a site is more likely to be colonized if more of its neighbors were previously occupied and if it provides more appealing environmental characteristics than its neighboring sites. Additionally, a site without occupied neighbors may also become colonized through the inclusion of a long‐distance dispersal process. Although similar model specifications have been developed for epidemiological applications, ours formally accounts for detectability using the well‐known occupancy modeling framework. After demonstrating the viability and potential of this new form of dynamic occupancy model in a simulation study, we use it to obtain inference for the ongoing Common Myna (Acridotheres tristis) invasion in South Africa. Our results suggest that the Common Myna continues to enlarge its distribution and its spread via short distance movement, rather than long‐distance dispersal. Overall, this new modeling framework provides a powerful tool for managers examining the drivers of colonization including short‐ vs. long‐distance dispersal, habitat quality, and distance from source populations.

Natural populations that are rare, cryptic or inaccessible provide a monumental challenge to monitoring, as adequate data are extremely difficult to collect. Surveys often encompass only a small portion of a population's range due to difficult terrain or inclement weather, especially for populations with extensive ranges. Thus, to maximise encounters, sampling efforts may be largely opportunistic or biased to accessible areas. The resulting sparse and spatially biased data may be difficult to model, standardise across years and incorporate into an assessment or management framework. However, in many monitoring programs, there are usually multiple threads of data that, though each may have its own limitations, can be synthesised to reveal important ecological processes. Here, we demonstrate a simple technique to incorporate two additional streams of data on the same population, telemetry and survey effort data, into capture‐recapture analyses to address spatiotemporal sampling bias using simulated data. Utilisation distributions (UDs) computed from telemetry data are overlaid with UDs of survey efforts, providing an ‘effort by animal space use’ overlap covariate for modelling detection in a Jolly–Seber open population model. Using simulated data, we found that our method resulted in more accurate and precise estimates of abundance than traditional capture‐recapture models. We then applied this method to a 16 year photo‐identification capture‐recapture dataset (n = 143 individuals) along with telemetry data (n = 44 satellite tag deployments) collected from the endangered population of false killer whales resident to the main Hawaiian Islands. Incorporating space use and effort into this analysis improved precision of abundance estimates relative to previous modelling endeavours.

Understanding what drives changes in wildlife demography is fundamental to the conservation and management of depleted or declining populations, though making inference about the intrinsic and extrinsic factors that influence survival and reproduction remains challenging. Here we use mark–resight data from 2000 to 2018 to examine the effects of environmental variability on age‐specific survival and natality for the endangered western distinct population segment (wDPS) of Steller sea lions (Eumetopias jubatus) in Alaska, USA. Though this population has been studied extensively over the last four decades, the causes of divergent abundance trends that have been observed across the wDPS range remain unknown. We developed a Bayesian multievent mark–resight model that accounts for female reproductive state uncertainty. Annual survival probabilities for male pups (0.44; 0.36–0.53), female yearlings (0.63; 0.49–0.73), and male yearlings (0.62; 0.51–0.71) born in the western portion of the wDPS range, estimated here for the first time, were lower than those in the eastern portion of the wDPS range, estimated as: male pups (0.69; 0.65–0.74), female yearlings (0.76; 0.71–0.81), and male yearlings (0.71; 0.65–0.78). There was a higher proportion of young female breeders in the western portion of the range, but overall natality was lower (0.69; 0.47–0.96) than in the eastern portion of the range (0.80; 0.74–0.84). Additionally, pup mass had a positive effect on pup survival in the eastern portion of the range and a negative effect in the western portion of the range, potentially due to earlier weaning of heavier pups. Local‐ and basin‐scale oceanographic features such as the Aleutian Low, the Arctic Oscillation Index, the North Pacific Gyre Oscillation, chlorophyll concentration, upwelling, and wind in certain seasons were correlated with vital rates. However, drawing strong inferences from these correlations is challenging given that relationships between ocean conditions and an adaptive top predator in a dynamic ecosystem are exceedingly complex. This study provides the first demographic rate estimates for the western portion of the range where abundance estimates continue to decline. These results will advance efforts to identify factors driving regionally divergent abundance trends, with implications for population‐level responses to future climate variability.

Adult male and female northern fur seals (Callorhinus ursinus) are sexually segregated in different regions of the North Pacific Ocean and Bering Sea during their winter migration. Explanations for this involve interplay between physiology, predator-prey dynamics, and ecosystem characteristics, however possible mechanisms lack empirical support. To investigate factors influencing the winter ecology of both sexes, we deployed five satellite-linked conductivity, temperature, and depth data loggers on adult males, and six satellite-linked depth data loggers and four satellite transmitters on adult females from St. Paul Island (Bering Sea, Alaska, USA) in October 2009. Males and females migrated to different regions of the North Pacific Ocean: males wintered in the Bering Sea and northern North Pacific Ocean, while females migrated to the Gulf of Alaska and California Current. Horizontal and vertical movement behaviors of both sexes were influenced by wind speed, season, light (sun and moon), and the ecosystem they occupied, although the expression of the behaviors differed between sexes. Male dive depths were aligned with the depth of the mixed layer during daylight periods and we suspect this was the case for females upon their arrival to the California Current. We suggest that females, because of their smaller size and physiological limitations, must avoid severe winters typical of the northern North Pacific Ocean and Bering Sea and migrate long distances to areas of more benign environmental conditions and where prey is shallower and more accessible. In contrast, males can better tolerate often extreme winter ocean conditions and exploit prey at depth because of their greater size and physiological capabilities. We believe these contrasting winter behaviors 1) are a consequence of evolutionary selection for large size in males, important to the acquisition and defense of territories against rivals during the breeding season, and 2) ease environmental/physiological constraints imposed on smaller females.

Ecologists often fit models to survey data to estimate and explain variation in animal abundance. Such models typically require that animal density remains constant across the landscape where sampling is being conducted, a potentially problematic assumption for animals inhabiting dynamic landscapes or otherwise exhibiting considerable spatiotemporal variation in density. We review several concepts from the burgeoning literature on spatiotemporal statistical models, including the nature of the temporal structure (i.e., descriptive or dynamical) and strategies for dimension reduction to promote computational tractability. We also review several features as they specifically relate to abundance estimation, including boundary conditions, population closure, choice of link function, and extrapolation of predicted relationships to unsampled areas. We then compare a suite of novel and existing spatiotemporal hierarchical models for animal count data that permit animal density to vary over space and time, including formulations motivated by resource selection and allowing for closed populations. We gauge the relative performance (bias, precision, computational demands) of alternative spatiotemporal models when confronted with simulated and real data sets from dynamic animal populations. For the latter, we analyze spotted seal ( Phoca largha ) counts from an aerial survey of the Bering Sea where the quantity and quality of suitable habitat (sea ice) changed dramatically while surveys were being conducted. Simulation analyses suggested that multiple types of spatiotemporal models provide reasonable inference (low positive bias, high precision) about animal abundance, but have potential for overestimating precision. Analysis of spotted seal data indicated that several model formulations, including those based on a log-Gaussian Cox process, had a tendency to overestimate abundance. By contrast, a model that included a population closure assumption and a scale prior on total abundance produced estimates that largely conformed to our a priori expectation. Although care must be taken to tailor models to match the study population and survey data available, we argue that hierarchical spatiotemporal statistical models represent a powerful way forward for estimating abundance and explaining variation in the distribution of dynamical populations.