Inferring resource selection and utilization distributions from irregular and error-prone animal tracking data

Abstract: Habitat selection and space use are fundamental to understanding animal distribution. Traditional methods for quantifying habitat preferences from telemetry data assume regular sampling and negligible measurement error. However, these assumptions are routinely violated in marine systems. Practitioners typically regularize and filter the data before fitting models, but these two-step procedures do not propagate uncertainty from the filtering stage and can yield biased estimates. Habitat-driven Langevin diffusion models offer an elegant alternative, naturally accommodating irregular sampling. However, incorporating measurement error via a state-space formulation is challenging because habitat covariates depend on the latent true locations. We address this using the Laplace approximation to simultaneously integrate over true locations and account for habitat covariates along latent paths, yielding a single-stage framework efficiently implemented in Template Model Builder (TMB). By doing so, we provide the first TMB implementation capable of handling covariates that depend on latent variables, allowing inference via fast and efficient maximum likelihood estimation. Simulations show that our approach outperforms the two-step method, recovering habitat-selection parameters even under substantial measurement error and missing data, with more accurate utilization distributions and trajectory reconstructions. Applied to narwhal (Monodon monoceros) telemetry data, the two-step method substantially shrinks the habitat selection coefficient towards zero, while our unified approach recovers a much stronger signal. Our framework offers a computationally efficient solution to long-standing challenges of measurement error and temporal irregularity in habitat selection inference, applicable across a wide range of taxa and environments.