A framework for the interaction between wildlife and spatial hazards

One of the major challenges in conservation and movement ecology is to understand the mechanisms through which spatial interventions due to human development can affect wildlife. An important example is the development of road infrastructure leading to wildlife-vehicle accidents. Modern tracking technology increasingly provides high-resolution datasets of the movement patterns of animals at various spatiotemporal scales, but theory lags behind in providing an understanding of how patterns lead to interactions. We develop a general theory for the interactions between a moving agent and a hazardous domain. Landscape scale motion is represented by stochastic differential equations, whereas interaction events are represented by stopping times for this process. Statistics of these stopping times provide trajectory-level information about the use of space in the vicinity of a hazard. General results about the distribution of interaction times can be derived, with particular emphasis on the case of range-resident motion, exemplified by the Ornstein-Uhlenbeck processes. Incorporating intrinsic sources of mortality allows for evaluation of the reduction in lifespan associated to the introduction of the spatial hazard. The importance of considering inhomogeneous use of space is highlighted by comparison with reflected Brownian motion. We discuss the connection with data and simulations, as well as possible extensions to include autocorrelation in noise.