In our more theoretical projects, we develop bottom-up mathematical frameworks to investigate how nonlinear feedbacks acting on individual movement and demographic rates shape population dynamics in space and time. We are particularly interested in understanding whether long-range attraction/repulsion and growth activation/inhibition are system-independent drivers of spatial self-organization. In these projects, we combine stochastic differential equations, random walk theory, coarse-graining methods, efficient algorithms for interacting-particle systems, and partial integro-differential equations.
We have shown how these long-range interactions can reverse competitive exclusion in Lotka-Volterra systems (Maciel & Martinez-Garcia, 2021) and favor the persistence of mutualistic communities at weaker interaction strengths (Bongestab et al., 2026). For single populations, we have shown that aggregation can increase resilience under environmental change in populations with Allee effects (Jorge & Martinez-Garcia, 2024), and how environmental flows shape spatial distributions and abundances (Silvano et al., 2025). A bias in individual movement across an asymmetric landscape changes both where a population concentrates and the critical habitat size it needs to persist (Dornelas et al., 2024). Most recently, we found that higher-order competition fosters the diversity of pattern shapes observed in competitive systems (Pinto-Ramos et al., 2026).