Modelling animal movement and habitat selection across scales

The study of animals’ movement is key to understand how their short-term decisions, driven by environmental factors, give rise to long-term population distributions. This field of research has grown rapidly due to increased availability of animal tracking data, e.g., from GPS collars. The development of statistical methods, including specification of biologically realistic models and computational approaches for model fitting, has lagged behind data collection. Statistical research is needed to harness the full potential of existing (and future) data sets, to understand the mechanisms of animal movement, and to predict animal distributions in a changing environment. One key shortcoming of existing models is that their formulation is tied to a given spatiotemporal scale, limiting our ability to understand how large-scale patterns emerge from small-scale events, to compare results across studies, and to combine data sources. I will develop a unifying statistical framework to model animal movement across scales, with two components: (1) mechanistic models linking animals’ movement decisions to the emerging distributions, and (2) continuous-time models based on stochastic differential equations (SDEs) to overcome dependence on the temporal scale of the data. I will demonstrate that irreversible stationary processes, recently proposed as an efficient way to sample from probability distributions, can be viewed as animal movement models, to provide a long-sought link between small-scale displacements and resulting large-scale spatial distribution. This research will lead to a method of joint inference for tracking and survey data (e.g., from camera traps), greatly increasing the statistical power of many ecological studies. I also propose increasing the utility and accessibility of SDEs in ecology, as their continuous-time formulation requires no limiting assumptions about the time resolution of the data, and describes the animal's actual movement process (rather than the discrete-time observation process). I will develop computationally-efficient approaches to improve inference for a wide class of flexible SDEs, providing an alternative to discrete-time models. This interdisciplinary project will produce cutting-edge statistical methods to analyse ecological data, and will be of broad interest in the mathematical and biological sciences. New general methods of inference for flexible SDEs, including time-varying dynamics, will have high impact in applied statistics, and in various areas where SDEs are used. This work will have direct impact in theoretical ecology, with a mathematical description of pattern formation in animal distributions, and in applied ecology, where continuous-time and multiscale approaches will become indispensable to leverage complex ecological data. Finally, this research will provide statistical tools for models used in physics and mathematical biology, with great potential for application beyond wildlife studies.