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 Two previously unpublished marine mammal telemetry data sets were analyzed to illustrate use of the model, by-products available from the analysis, and different modifications which are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.

Abstract. 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 logitnormal 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.

Summary. We propose a general framework for the analysis of animal telemetry data through the use of weighted distributions. It is shown that several interpretations of resource selection functions arise when constructed from the ratio of a use and availability distribution. Through the proposed general framework, several popular resource selection models are shown to be special cases of the general model by making assumptions about animal movement and behavior. The weighted distribution framework is shown to be easily extended to readily account for telemetry data that are highly autocorrelated; as is typical with use of new technology such as global positioning systems animal relocations. An analysis of simulated data using several models constructed within the proposed framework is also presented to illustrate the possible gains from the flexible modeling framework. The proposed model is applied to a brown bear data set from southeast Alaska.

Summary 1.We describe an open-source R package, marked, for analysis of mark-recapture data to estimate survival and animal abundance. 2. Currently, marked is capable of fitting Cormack-Jolly-Seber (CJS) and Jolly-Seber models with maximum likelihood estimation (MLE) and CJS models with Bayesian Markov Chain Monte Carlo methods. The CJS models can be fitted with MLE using optimization code in R or with Automatic Differentiation Model Builder. The latter allows incorporation of random effects. 3. Some package features include: (i) individual-specific time intervals between sampling occasions, (ii) generation of optimization starting values from generalized linear model approximations and (iii) prediction of demographic parameters associated with unique combinations of individual and time-specific covariates. 4. We demonstrate marked with a commonly analysed European dipper (Cinclus cinclus) data set. 5. The package will be most useful to ecologists with large mark-recapture data sets and many individual covariates.

Contemporary ecologists often find themselves with an overwhelming amount of data to analyze. For example, it is now possible to collect nearly continuous spatiotemporal data on animal locations via global positioning systems and other satellite telemetry technology. In addition, there is a wealth of readily available environmental data via geographic information systems and remote sensing. We present a modeling framework that utilizes these forms of data and builds on previous research pertaining to the quantitative analysis of animal movement. This approach provides additional insight into the environmental drivers of residence and movement as well as resource selection while accommodating path uncertainty. The methods are demonstrated in an application involving mule deer movement in the La Sal Range, Utah, USA. Supplemental materials for this article are available online.

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.

Summary. We consider a fully model-based approach for the analysis of distance sampling data. Distance sampling has been widely used to estimate abundance (or density) of animals or plants in a spatially explicit study area. There is, however, no readily available method of making statistical inference on the relationships between abundance and environmental covariates. Spatial Poisson process likelihoods can be used to simultaneously estimate detection and intensity parameters by modeling distance sampling data as a thinned spatial point process. A model-based spatial approach to distance sampling data has three main benefits: it allows complex and opportunistic transect designs to be employed, it allows estimation of abundance in small subregions, and it provides a framework to assess the effects of habitat or experimental manipulation on density. We demonstrate the model-based methodology with a small simulation study and analysis of the Dubbo weed data set. In addition, a simple ad hoc method for handling overdispersion is also proposed. The simulation study showed that the model-based approach compared favorably to conventional distance sampling methods for abundance estimation. In addition, the overdispersion correction performed adequately when the number of transects was high. Analysis of the Dubbo data set indicated a transect effect on abundance via Akaike's information criterion model selection. Further goodness-of-fit analysis, however, indicated some potential confounding of intensity with the detection function.

Abstract. Checking that models adequately represent data is an essential component