Efficient approximate Bayesian inference for quantifying uncertainty in multiscale animal movement models

It is becoming increasingly important for wildlife managers and conservation ecologists to understand which resources are selected or avoided by an animal and how to best predict future spatial distributions of animal populations in the long term. However, inferring the patterns of space use by animals is a challenging multiscale inference problem, and formal uncertainty quantification of parameter estimates is an essential component of models that provide useful predictions across scales. In this study, we develop an approximate Bayesian inference framework for step selection models of animal movement which quantifies the uncertainty in estimates of resource selection and avoidance parameters within the Bayesian paradigm. The framework allows joint inference of movement and resource selection parameters of animals and is multiscale in that parameters inferred from fine scale movement steps scale to produce predictions of long-term patterns of space use. Our analysis focuses on simulated movement data in which we test the performance of our framework by altering movement parameters in the data-generating process. In our simulations, individuals respond to two environmental covariates and we employ all combinations of positive and negative selection coefficients corresponding to attraction to an environmental feature and avoidance of an environmental feature, respectively. In all scenarios, we recover the movement parameters used for the simulation of synthetic movement data using variational inference, an approximate Bayesian method, allowing us to formally quantify the uncertainty associated with each parameter for varying data set sizes. Our framework successfully recovered all combinations of movement parameters of the simulated data and accurately captured their posterior distributions given the available data suggesting that the framework is reliable and suitable for inferring how animals select resources and move on a landscape. Notably, our analysis shows that even for reasonably large data sets (circa 10,000 observations) there can still be considerable uncertainty associated with resource selection parameters which can in turn lead to inaccurate predictions of long term space use if not properly incorporated into the modelling approach. To further illustrate the utility of our approach, we also present a case study of its application to an example data set consisting of GPS locations of a fisher ( Martes pennanti ). Our approach will be of interest to ecologists looking to address conservation questions such as when and where animals are likely to spend most of their time. Furthermore, the approach could be used to predict new suitable areas for conservation based on how GPS collared animals use or avoid resources while including uncertainty around the predictions, thereby helping to make informed management decisions. • Bayesian inference is used to quantify uncertainty in an animal movement model. • We use variational inference to obtain posterior distributions of parameters. • Substantial levels of uncertainty are observed for even large telemetry datasets.