Dynamics of Complex Living Systems

Spatial mathematical ecology

Research

Our theoretical projects have shown the potential impact of long-range (i.e., non-local) interactions in shaping ecological dynamics at different scales, from the formation of different spatial patterns of population density during the lifetime of a single generation to reverting the outcome of species interactions over many generations. Some of our recent advances have shown that aggregation might increase the resilience of populations exhibitin. Allee effects when they are exposed to environmental changes. We have also developed spatial theories to investigate species competition and show that self-organized pattern formation may allow for species coexistence in conditions where non-spatial theories predict the competitive exclusion of one of the competitors.

Selected references:

Jorge, D. C. P., & Martinez-Garcia, R. (2023). Demographic effects of aggregation in the presence of a component Allee effect. arXiv preprint arXiv:2305.1341.
Maciel, G. A., & Martinez-Garcia, R. (2021). Enhanced species coexistence in Lotka-Volterra competition models due to nonlocal interactions. Journal of Theoretical Biology, 530, 110872.
Martinez-Garcia, R., López, C., & Vazquez, F. (2021). Species exclusion and coexistence in a noisy voter model with a competition-colonization tradeoff. Physical Review E, 103(3), 032406.