Characterizing Migration Dynamics with Convolution-Based Movement Models

Migratory animals often exhibit changes in their behavior during their migration. Telemetry data provide a way to observe geographic animal positions over time, but not necessarily changes in the dynamics in the movement process. Continuous-time continuous-space animal movement models provide a statistical framework for learning about individual-based animal movement dynamics. Continuous-time models also allow for statistical predictions of the trajectory during periods when the telemetry device did not record the animal's position and in the presence of location error. Predicted trajectories can be inferred using continuous-time models, but models capable of mimicking realistic trajectories with sufficient detail are computationally challenging to fit to large data sets. 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 animal movement trajectories. Our approach uses so-called process convolutions to allow for flexibility in the movement process while facilitating implementation and incorporating location uncertainty. We review convolution-based approaches to account for nonstationarity in continuous-time animal movement models including temporal deformation and nested process convolutions. We demonstrate these approaches in two case studies involving migratory birds. Specifically, we use temporal deformation to account for heterogeneity in individual greater white-fronted goose migrations in Europe and Iceland and we use nested process convolutions to model dynamic migratory networks in sandhill cranes in North America.