Three-Dimensional Correlated Random Walks for Animal Movement and Habitat Selection

Animal movement and habitat selection underpin important ecological phenomena, from individual behaviour to population-level distributions. Despite navigating three-dimensional space, animals' movement is typically measured and analysed on a two-dimensional plane, which limits our understanding of species that swim or fly. Therefore, we propose a step selection function (SSF) capable of quantifying animal movement and habitat selection in three dimensions. We formulate a very general family of three-dimensional correlated random walks, aimed at capturing unique features of three-dimensional data. Using Antarctic petrel data, we illustrate how these SSFs can be used to assess selection for vertically-stratified habitat, account for barriers (e.g., the ground or ocean surface), and model attraction to any number of directional targets. Our modelling framework provides a solid foundation for three-dimensional analyses, which will be crucial to answer ecological questions that would otherwise be ignored in two dimensions.