Sine-skewed von Mises- and Lindley/Gumbel models as candidates for direction and distance in modelling animal movement

Abstract

Movement of animals is often characterised by direction (measured on the circle) and distance (measured on the real line); but traditionally employed models often do not account for potential asymmetric directional movement, or departures from the usual von Mises assumption for direction and gamma/Weibull assumptions for distance. This paper focuses on the modelling of circular data in this animal movement context relying on a previously unconsidered circular distribution (the sine-skewed von Mises) which provides a platform for departures from symmetry. In addition, alternative models to usual distance assumptions are considered, namely the power Lindley (as a mixture of gamma andWeibull distributions) as well as a Gumbel candidate. Computational aspects and investigations of this joint modelling (presented as a consensus model) are highlighted, accompanied by an extensive bootstrap study. A general hidden state Markov model is used to incorporate these essential components when estimating via the use of the EM algorithm, and goodness of fit measures verify the validity and viable future consideration of the newly proposed theoretical models within this practical and computational animal movement environment.