title: Uncovering periodic patterns of space use in animal tracking data with periodograms, including a new algorithm for the Lomb-Scargle periodogram and improved randomization tests.
abstract: BACKGROUND
  Periodicity in activity level (rest/activity cycles) is ubiquitous in nature, but whether and how these periodicities translate into periodic patterns of space use by animals is much less documented. Here we introduce an analytical protocol based on the Lomb-Scargle periodogram (LSP) to facilitate exploration of animal tracking datasets for periodic patterns. The LSP accommodates missing observations and variation in the sampling intervals of the location time series.
  
  
  RESULTS
  We describe a new, fast algorithm to compute the LSP. The gain in speed compared to other R implementations of the LSP makes it tractable to analyze long datasets (>10(6) records). We also give a detailed primer on periodicity analysis, focusing on the specificities of movement data. In particular, we warn against the risk of flawed inference when the sampling schedule creates artefactual periodicities and we introduce a new statistical test of periodicity that accommodates temporally autocorrelated background noise. Applying our LSP-based analytical protocol to tracking data from three species revealed that an ungulate exhibited periodicity in its movement speed but not in its locations, that a central place-foraging seabird tracked moon phase, and that the movements of a range-resident canid included a daily patrolling component that was initially masked by the stochasticity of the movements.
  
  
  CONCLUSIONS
  The new, fast algorithm tailored for movement data analysis and now available in the R-package ctmm makes the LSP a convenient exploratory tool to detect periodic patterns in animal movement data.
authors.affiliation: Smithsonian Conservation Biology Institute, National Zoological Park, Front Royal, VA 22630 USA.
authors.forename: Guillaume
authors.initials: G
authors.lastname: Péron
authors.affiliation: Smithsonian Conservation Biology Institute, National Zoological Park, Front Royal, VA 22630 USA.|Department of Biology, University of Maryland, College Park, MD 20742 USA.
authors.forename: Chris H
authors.initials: CH
authors.lastname: Fleming
authors.affiliation: National Research Center for Carnivore Conservation (CENAP/ICMBio), Atibaia, Sao Paulo Brazil.
authors.forename: Rogerio C
authors.initials: RC
authors.lastname: de Paula
authors.affiliation: Smithsonian Conservation Biology Institute, National Zoological Park, Front Royal, VA 22630 USA.|Department of Biology, University of Maryland, College Park, MD 20742 USA.
authors.forename: Justin M
authors.initials: JM
authors.lastname: Calabrese
keywords: Activity cycles; Autocorrelation; Behavior; Central place foraging; Circadian; Periodicity