Movement Ecology and Encounter Theory

Movement determines where animals go, whom they meet, and ultimately how populations and communities are structured. At the same time, movement is among the ecological processes that human pressure disrupts most directly. Mammals in landscapes with a high human footprint move only one-half to one-third as far as those where that footprint is low (Tucker et al., Science 2018), and 49% of the migratory populations listed under the UN Convention on Migratory Species are now declining, with 24% facing extinction (CMS, 2026).

Despite movement's ecological importance, a large body of ecological theory assumes that individuals move uniformly within the landscape and that interactions follow a random-encounter process. This assumption is central to Verhulst's equation for logistic growth and Lotka-Volterra models, yet it overlooks that animals exhibit different patterns of space use. In many species, for example, animals move within home ranges smaller than the population range, overlapping only partially with those of their neighbors.

We apply stochastic calculus to investigate how patterns of individual movement, observed in animal tracking datasets, determine interactions among individuals and between individuals and landscape features such as roads or fences (Garcia de Figueiredo et al., 2026). We have produced a new family of encounter models accounting for real movement behavior and shown how more realistic encounter rates can be higher or lower than mass-action predictions depending on home-range spatial organization (Martinez-Garcia et al., 2020; Surendran et al., 2026).

To bring these models closer to ecological applications, we used them to develop a statistical estimator of the spatial distribution of encounters (Noonan et al., 2021) and to establish what single trajectories can reveal about the interactions they drive (Garcia de Figueiredo et al., 2024). At larger scales, we have also investigated how these encounters shape population dynamics, showing how range-resident movement can determine population abundances once it is embedded in a logistic model for population growth (Menezes et al., 2025).

Selected Publications

• A. Surendran, L. Ramirez, J.M. Calabrese, W.F. Fagan, R. Martinez-Garcia. Range residency determines how movement persistence shapes encounter rates. arXiv:2510.13017 (2026) (PDF).
• B. Garcia de Figueiredo, I. Silva, M.J. Noonan, C.H. Fleming, W.F. Fagan, J.M. Calabrese, R. Martinez-Garcia. How animal movement influences wildlife-vehicle collision risk: a mathematical framework for range-resident species. Journal of Theoretical Biology 627, 112471 (2026) (PDF).
• R. Menezes, J.M. Calabrese, W.F. Fagan, R. Martinez-Garcia. The range-resident logistic model: a new framework to formalize the population-dynamics consequences of range residency. Ecology Letters 28(12), e70269 (2025) (PDF).
• B. Garcia de Figueiredo, J.M. Calabrese, W.F. Fagan, R. Martinez-Garcia. Ergodicity shapes inference in biological reactions driven by a latent trajectory. arXiv:2409.11433 (2024) (PDF).
• M.J. Noonan, R. Martinez-Garcia, G.H. Davis, M.C. Crofoot, R. Kays, B.T. Hirsch, E. Payne, A. Sih, D.L. Sinn, O. Spiegel, W.F. Fagan, C.H. Fleming, J.M. Calabrese. Estimating encounter location distributions from animal tracking data. Methods in Ecology and Evolution 12(7), 1158–1173 (2021) (PDF).
• R. Martinez-Garcia, C.H. Fleming, R. Seppelt, W.F. Fagan, J.M. Calabrese. How range-residency and long-range perception change encounter rates. Journal of Theoretical Biology 498, 110267 (2020) (PDF).