Towards transient space-use dynamics: re-envisioning models of utilization distribution and their applications.

Background: Models of utilization distribution in the form of partial differential equations have long contributed to our understanding of organismal space use patterns. In studies of infectious diseases, they are also being increasingly adopted in support of epidemic forecasting and scenario planning. However, as movement research shifts its focus towards large data collection and statistical modeling of movement trajectories, the development of such models has notably slowed.

Methods: Here, we demonstrate the continued importance of modeling utilization distribution to predict variation in space-use patterns over time. We highlight the considerable, yet largely untapped, potential of such models, which have historically been limited by the steady-state assumption due to longstanding technical constraints. Now, by adapting existing computational tools primarily developed for material science and engineering, we can probe beyond the steady states and unlock from them a broad spectrum of complex, transient space-use dynamics. Our approach requires little experience in numerical analysis and is readily accessible to model practitioners in ecology and epidemiology across diverse systems where movement is a critical feature.

Results: We illustrated our approach using a mix of canonical and novel case studies, covering topics from wildlife translocation to vaccine deployment. First, we revisited a classical model of canid territorial formation driven by scent-mediated conspecific avoidance. Transient space-use analysis uncovered previously hidden spatial dynamics that are ecologically informative. Next, we applied our approach to long-distance movement on realistic landscapes. Habitat and land-use heterogeneities markedly affected the transient space-use dynamics and short-term forecasts, even when the steady state remained unchanged, with direct implications for conservation management. Finally, we modeled transient space-use dynamics as both a response to and a driver of transient population dynamics. The importance of this interdependence was shown in the context of epidemiology, in a scenario where the movement of healthcare personnel is influenced by local outbreak conditions that are stochastically evolving.

Conclusions: By facilitating transient space-use analysis, our approach could lead to reevaluations of foundational ecological concepts such as home range and territory, replacing static with dynamic definitions that more accurately reflect biological realities. Furthermore, we contend that a growing interest in transient space-use dynamics, spurred by this work, could have transformative effects, stimulating new research avenues in ecology and epidemiology.