Restrictions on roaming Until the past century or so, the movement of wild animals was relatively unrestricted, and their travels contributed substantially to ecological processes. As humans have increasingly altered natural habitats, natural animal movements have been restricted. Tucker et al. examined GPS locations for more than 50 species. In general, animal movements were shorter in areas with high human impact, likely owing to changed behaviors and physical limitations. Besides affecting the species themselves, such changes could have wider effects by limiting the movement of nutrients and altering ecological interactions. Science , this issue p. 466

Summary1. Movement ecology has developed rapidly over the past decade, driven by advances in tracking technology that have largely removed data limitations. Development of rigorous analytical tools has lagged behind empirical progress, and as a result, relocation data sets have been underutilized. 2. Discrete-time correlated random walk models (CRW) have long served as the foundation for analyzing relocation data. Unfortunately, CRWs confound the sampling and movement processes. CRW parameter estimates thus depend sensitively on the sampling schedule, which makes it difficult to draw sampling-independent inferences about the underlying movement process. Furthermore, CRWs cannot accommodate the multiscale autocorrelations that typify modern, finely sampled relocation data sets. 3. Recent developments in modelling movement as a continuous-time stochastic process (CTSP) solve these problems, but the mathematical difficulty of using CTSPs has limited their adoption in ecology. To remove this roadblock, we introduce the ctmm package for the R statistical computing environment. ctmm implements all of the CTSPs currently in use in the ecological literature and couples them with powerful statistical methods for autocorrelated data adapted from geostatistics and signal processing, including variograms, periodograms and non-Markovian maximum likelihood estimation. 4. ctmm is built around a standard workflow that begins with visual diagnostics, proceeds to candidate model identification, and then to maximum likelihood fitting and AIC-based model selection. Once an accurate CTSP for the data has been fitted and selected, analyses that require such a model, such as quantifying home range areas via autocorrelated kernel density estimation or estimating occurrence distributions via time-series Kriging, can then be performed. 5. We use a case study with African buffalo to demonstrate the capabilities of ctmm and highlight the steps of a typical CTSP movement analysis workflow.

A goal of animal movement analysis is to reveal behavioural mechanisms by which organisms utilize complex and variable environments. Statistical analysis of movement data is complicated by the fact that the data are multidimensional, autocorrelated and often marked by error and irregular measurement intervals or gappiness. Furthermore, movement data reflect behaviours that are themselves heterogeneous. Here, we model movement data as a subsampling of a continuous stochastic processes, and introduce the behavioural change point analysis (BCPA), a likelihood-based method that allows for the identification of significant structural changes. The BCPA is robust to gappiness and measurement error, computationally efficient, easy to implement and reveals structure that is otherwise difficult to discern. We apply the analysis to a GPS movement track of a northern fur seal (Callorhinus ursinus), revealing an unexpectedly complex diurnal behavioural profile, and demonstrate its robustness to the greater errors associated with the ARGOS tracking system. By informing empirical interpretation of movement data, we suggest that the BCPA can eventually motivate the development of mechanistic behavioural models.

Movement data provide a window - often our only window - into the cognitive, social and biological processes that underlie the behavioural ecology of animals in the wild. Robust methods for identifying and interpreting distinct modes of movement behaviour are of great importance, but complicated by the fact that movement data are complex, multivariate and dependent. Many different approaches to exploratory analysis of movement have been developed to answer similar questions, and practitioners are often at a loss for how to choose an appropriate tool for a specific question. We apply and compare four methodological approaches: first passage time (FPT), Bayesian partitioning of Markov models (BPMM), behavioural change point analysis (BCPA) and a fitted multistate random walk (MRW) to three simulated tracks and two animal trajectories - a sea lamprey (Petromyzon marinus) tracked for 12 h and a wolf (Canis lupus) tracked for 1 year. The simulations - in which, respectively, velocity, tortuosity and spatial bias change - highlight the sensitivity of all methods to model misspecification. Methods that do not account for autocorrelation in the movement variables lead to spurious change points, while methods that do not account for spatial bias completely miss changes in orientation. When applied to the animal data, the methods broadly agree on the structure of the movement behaviours. Important discrepancies, however, reflect differences in the assumptions and nature of the outputs. Important trade-offs are between the strength of the a priori assumptions (low in BCPA, high in MRW), complexity of output (high in the BCPA, low in the BPMM and MRW) and explanatory potential (highest in the MRW). The animal track analysis suggests some general principles for the exploratory analysis of movement data, including ways to exploit the strengths of the various methods. We argue for close and detailed exploratory analysis of movement before fitting complex movement models.