Animal movement models for migratory individuals and groups

Abstract

Animals often exhibit changes in their behaviour during migration. Telemetry data provide a way to observe geographic position of animals over time, but not necessarily changes in the dynamics of the movement process. Continuous-time models allow for statistical predictions of the trajectory in the presence of measurement error and during periods when the telemetry device did not record the animal's position. However, continuous-time models capable of mimicking realistic trajectories with sufficient detail are computationally challenging to fit to large datasets. Furthermore, basic continuous-time model specifications (e.g. Brownian motion) lack realism in their ability to capture nonstationary dynamics. We present a unified class of animal movement models that are computationally efficient and provide a suite of approaches for accommodating nonstationarity in continuous trajectories due to migration and interactions among individuals. Our approach uses process convolutions to allow for flexibility in the movement process while facilitating implementation and incorporating location uncertainty. We show how to nest convolution models to incorporate interactions among migrating individuals to account for nonstationarity and provide inference about dynamic migratory networks. We demonstrate these approaches in two case studies involving migratory birds. Specifically, we used process convolution models with temporal deformation to account for heterogeneity in individual greater white-fronted goose migrations in Europe and Iceland, and we used nested process convolutions to model dynamic migratory networks in sandhill cranes in North America. The approach we present accounts for various forms of temporal heterogeneity in animal movement and is not limited to migratory applications. Furthermore, our models rely on well-established principles for modelling-dependent data and leverage modern approaches for modelling dynamic networks to help explain animal movement and social interaction.