Correlated velocity models as a fundamental unit of animal movement: synthesis and applications

Eliezer Gurarie,Jesús Hernández-Pliego,Christen H Fleming,Kristin L Laidre,William F Fagan,Otso Ovaskainen

doi:10.1186/s40462-017-0103-3

Abstract

BackgroundContinuous time movement models resolve many of the problems with scaling, sampling, and interpretation that affect discrete movement models. They can, however, be challenging to estimate, have been presented in inconsistent ways, and are not widely used.MethodsWe review the literature on integrated Ornstein-Uhlenbeck velocity models and propose four fundamental correlated velocity movement models (CVM’s): random, advective, rotational, and rotational-advective. The models are defined in terms of biologically meaningful speeds and time scales of autocorrelation. We summarize several approaches to estimating the models, and apply these tools for the higher order task of behavioral partitioning via change point analysis.ResultsAn array of simulation illustrate the precision and accuracy of the estimation tools. An analysis of a swimming track of a bowhead whale (Balaena mysticetus) illustrates their robustness to irregular and sparse sampling and identifies switches between slower and faster, and directed vs. random movements. An analysis of a short flight of a lesser kestrel (Falco naumanni) identifies exact moments when switches occur between loopy, thermal soaring and directed flapping or gliding flights.ConclusionsWe provide tools to estimate parameters and perform change point analyses in continuous time movement models as an R package (smoove). These resources, together with the synthesis, should facilitate the wider application and development of correlated velocity models among movement ecologists.

Highlights

Continuous time movement models resolve many of the problems with scaling, sampling, and interpretation that affect discrete movement models
Our primary goal in this paper is to argue for the flexibility and appropriateness of Correlated Velocity Movement (CVM) models as a “fundamental unit” of movement
Hierarchical family of CVM models defined in terms of biologically intuitive parameters, notably speeds and characteristic time scales

Summary

Introduction

Continuous time movement models resolve many of the problems with scaling, sampling, and interpretation that affect discrete movement models. They can, be challenging to estimate, have been presented in inconsistent ways, and are not widely used. The correlated random walk (CRW), first proposed by Patlak [4] and reintroduced by Kareiva and Shigesada [5], models observed location data in terms of distributions for step lengths and turning angles. The observed axial persistence of most movements (at some unspecified scale) is modeled with a parameter that quantifies the extent to which turning angles cluster around zero degrees. In most applications of CRWs, consecutive turning angles and step-lengths are assumed to be independent [2, 6] (though see [7])

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