Absorption statistics of movement models with home-ranging behavior: animal-vehicle collisions as a case study.

A lot of ecological theory relies on ordinary-differential-equation models that assume well-mixed systems and do not incorporate any information about the spatial distribution of organisms. However, ecosystems present spatial heterogeneities at different scales that can impact individual fitness and, ultimately, population dynamics. I will present an alternative approach to describe the spatiotemporal dynamics of a population of interacting agents. To this end, I will consider a system with nonlinear birth-death rates and positive and negative inter-individual interactions acting at different spatial ranges. I will first describe the stochastic, individual-level rules that govern the reproduction and death of each individual. Then, using field-theory techniques, I will derive a non-local partial differential equation for the population density and compare its predictions with those obtained assuming well-mixed populations. Finally, I will discuss the ecological relevance of our results and how this approach can be extended to more complex scenarios.