ctmm: anrpackage for analyzing animal relocation data as a continuous‐time stochastic process

Abstract

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.

Space Use and Movement of a Neotropical Top Predator: The Endangered Jaguar

“…We calculated variograms, fit movement models, and estimated home ranges using the ctmm package [25,41] in the R environment for statistical computing [42]. For each animal, we plotted the estimated semi-variance (function variogram ) as a function of time lag to visually inspect the autocorrelation structure of the location data [27].…”

“…At zero to short time lags, a linear increase in the semi-variance corresponds to uncorrelated velocity, suggesting movement models such as Brownian motion (BM) or Ornstein-Uhlenbeck (OU). Upward curvature at these time lags indicates velocity autocorrelation and suggests movement models such as Integrated OU (IOU) or OU with foraging (OUF) [25,27]. Space use was investigated by inspecting the behavior across longer time lags.…”

“…Both tools have limitations that are often not acknowledged. MCPs, for example, lack any underlying probabilistic model while KDEs are derived under the assumption of independent and identically distributed data (IID), a process that assumes uncorrelated positions and velocities and which cannot be recognized as a movement model [11,25]. Incorporating autocorrelated data in conventional KDE frameworks has the potential to underestimate the size of animal home ranges, especially as the temporal frequency of positions collected increases [11]—a situation common with modern GPS tracking devices.…”

“…Movement analyses using this method have a number of desirable properties, including the ability to handle irregular sampling schedules (including gaps in the data) and complex autocorrelation structures [25,27–29]. This approach includes variogram analysis [27] and non-Markovian maximum likelihood estimation [28].…”

“…Calabrese et al . (2016) [25] give a detailed account of using the continuous-time movement modeling ( ctmm ) R package to perform this sequence of analyses.…”