The movement of animals is restricted to the aerial, aquatic, subterranean, and terrestrial spatial domains to which they are evolutionarily adapted. Within each spatial domain, animals can move among landscapes comprised of fractals exceeding two dimensions (i.e., 2D+). Prevailing quantitative techniques however, tend to predict animal movement in 2D. This tendency provides the implicit assumption that animals move over flat planes. In reality, real-world ecosystems are rarely that simplistic. Thus, analytical reduction of landscape complexity to 2D represents a considerable, and largely unnoticed, source of bias in the ecological modelling of animal movement data. We present this nuanced description of animal movement across multiple spatial domains and multiple dimensions and discuss the implications of the biases that are inherent to much of the prevailing ecological modelling of animal spatial ecology.