Benjamin Garcia de Figueiredo

arXiv2026

How animal movement influences wildlife-vehicle collision risk: a mathematical framework for range-resident species

Wildlife-vehicle collisions (WVC) threaten both biodiversity and human safety worldwide. Despite empirical efforts to characterize the major determinants of WVC risk and optimize mitigation strategies, we still lack a theoretical framework linking traffic, landscape, and individual movement features to collision risk. Here, we introduce such a framework by leveraging recent advances in movement ecology and reaction-diffusion stochastic processes with partially absorbing boundaries. Focusing on range-resident terrestrial mammals -- responsible for most fatal WVCs -- we model interactions with a single linear road and derive exact expressions for key survival statistics, including mean collision time and road-induced lifespan reduction. These quantities are expressed in terms of measurable parameters, such as traffic intensity or road width, and movement parameters that can be robustly estimated from relocation data, such as home-range crossing times, home-range sizes, or distance between home-range center and road. Therefore, our work provides an effective theoretical framework integrating movement and road ecology, laying the foundation for data-driven, evidence-based strategies to mitigate WVCs and promote safer, more sustainable transportation networks.

q-bio.PE↗

arXiv2025

Ergodicity shapes inference in biological reactions driven by a latent trajectory

Many natural phenomena are quantified by counts of observable events, from the annihilation of quasiparticles in a lattice to predator-prey encounters on a landscape to spikes in a neural network. These events are triggered at random intervals, when an underlying, often unobserved and therefore latent, dynamical system occupies a set of reactive states within its phase space. We show how the ergodicity of this latent dynamical system, i.e. existence of a well-behaved limiting stationary distribution, constrains the statistics of the reaction counts. This formulation makes explicit the conditions under which the counting process approaches a limiting Poisson process, a subject of debate in the application of counting processes to different fields. We show that the overdispersal relative to this limit encodes properties of the latent trajectory through its hitting times. These results set bounds on how information about a latent process can be inferred from a local detector, which we explore for two biophysical scenarios. First, in estimating an animal's activity level by how often it crosses a detector, we show how the mean count can fail to give any information on movement parameters, which are encoded in higher order moments. Second, we show how the variance of the inter-reaction time sets a fundamental limit on how precisely the size of a population of trajectories can be inferred by a detector, vastly generalizing the Berg-Purcell limit for chemosensation. Overall, we develop a flexible theoretical framework to quantify inter-event time distributions in reaction-diffusion systems that clarifies existing debates in the literature and explicitly shows which properties of latent processes can be inferred from observed reactions.

cond-mat.stat-mech↗