Dynamics of Complex Living Systems

In the more theoretical projects, we develop bottom-up mathematical frameworks to investigate how different nonlinear feedbacks acting on individual movement and demographic rates impact population dynamics in space and time. Our ultimate goal is to understand to what extent long-range attraction/repulsion and growth activation/inhibition are potential system-independent drivers of spatial self-organization in ecological systems. We describe these processes starting at the individual level, accounting for their inherent stochasticity, and use statistical mechanics and field theories to upscale these microscopic models to the population, community, and ecosystem levels. Therefore, our research on this topic uses various mathematical and computational techniques, such as individual-based simulations, stochastic differential equations and random walk theory, discrete interacting-particle systems, or partial integro-differential equations.

Microbial systems are ideal for studying emergent phenomena in ecological systems due to their fast characteristic time scales and the possibility of manipulating them in the laboratory. Within microbial systems, our group has extensively investigated the ecology and evolution of social behaviors in multicellular colonies, using Dictyostelium discoideum aggregates and flagellum-repressed Vibrio cholerae biofilms as model organisms. Combining various spatially explicit stochastic models, both on and off-lattice, and the analysis of microscopy images obtained in experimental setups, we are working to identify the feedbacks between microbial traits (adhesiveness, shape, motility…), behaviors (quorum-sensing regulated exoproduct release, dispersal strategies…), and environmental features might favor the evolution of social behaviors.

At much larger spatiotemporal scales than microbial systems, arid ecosystems exhibit similar self-organized patterns of vegetation density. The shapes of these patterns correlate very strongly with water availability, suggesting that they could inform about the proximity of impending desertification processes. Our research focuses on quantifying the causes and consequences of such patterns, providing several potential mechanisms to explain how they form, and testing these mechanisms with data gathered at different scales. At the ecosystem level, we test model predictions of ecosystem dynamics due to vegetation patterning using satellite images and remotely sensed time-series datasets. At the plant individual level, we develop root growth biophysical models and use them to predict, using game-theoretical arguments, expected root distributions in different environmental contexts. We ultimately test these predictions in greenhouse experiments and with root systems reconstructed in field surveys conducted by our collaborators at the Universidad Rey Juan Carlos in Madrid (Spain).

At the interface between water-limited landscapes and microbial systems regarding high-quality data availability, movement ecology combines high-quality data with the study of ecological systems in natural, uncontrolled conditions. Our group applies stochastic calculus to investigate how patterns of individual movement observed in animal tracking datasets determine the interactions among individuals and between individual and different landscape features, such as roads or fences. We are developing this project in close collaboration with our colleagues at the Earth System Science group, which allows us to incorporate much of our theory developments into widely used software packages for identifying and fitting movement models to animal tracking data.