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 Two previously unpublished marine mammal telemetry data sets were analyzed to illustrate use of the model, by-products available from the analysis, and different modifications which are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