Leveraging PDE solver for predicting transient space-use dynamics in ecological and epidemiological systems

Model predictions of animal and human space-use patterns stemming from individual-level movement behaviors have not only contributed significantly to our understanding of population and community dynamics, but they could also inform the development of conservation, natural resource management, and disease control policies. The recent proliferation of high-resolution movement data has ushered in a paradigm shift in how space use is considered: instead of being defined narrowly as the stationary, long-term distribution of individual locations, there is a growing recognition of its transient dynamics, e.g.., how space-use pattern varies before it eventually stabilizes. However, movement models are slow to follow due to longstanding technical challenges in solving transient space-use dynamics. Here, we introduce a numerical framework that enables transient analysis of mechanistic movement models based on partial differential (Fokker-Planck) equations. We demonstrate its potential applications in the context of general research questions in movement ecology using classical and new case studies as illustrations. We demonstrate the frameworks applications and versatility in classical home range models, but also show how it may be extended to address new ecological questions.