Our research focuses on understanding how organisms explore and respond to their local environment and how these responses shape the outcome of larger-scale ecological processes, such as population abundances, species distributions, or ecosystem resilience. Using the mathematical formalism of statistical mechanics and intensive numerical simulations, our ultimate goal is to discern to what extent these larger-scale processes are emergent phenomena determined by organism-level behaviors and formalize this upscaling into unifying theoretical frameworks. We work on a diversity of systems across various scales, but our primary focus has recently been on large terrestrial mammals exhibiting range-resident movement and dryland vegetation, where spatial patterns can be strikingly regular. In each of these systems, we develop mathematical models that we validate using various types of empirical data, and then use these models to make new, testable predictions. Therefore, we often work closely with experimentalists and field ecologists through an extensive network of collaborators that we have built over the year and that we are always eager to extend. Below, you can find more information on various projects and work on specific systems.
Spatial Population Dynamics
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 techniques from many-body physics to upscale these microscopic models to the population level. Therefore, in these projects, we use 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.
Our results have shown the potential impact of long-range (i.e., non-local) interactions and dispersal in shaping ecological dynamics at different scales, from the formation of different spatial patterns of population density during the lifetime of a single generation (Martinez-Garcia et al., 2015; Dornelas, de Castro et al., 2024) to reverting the outcome of competitive exclusion in competitive communities (Martinez-Garcia et al., 2021; Maciel and Martinez-Garcia, 2021). Some of our recent advances have shown that aggregation might increase the resilience of populations exhibiting Allee effects when they are exposed to environmental changes (Jorge & Martinez-Garcia 2024) and how external factors, such as environmental flows, shape population spatial distributions and abundances (Silvano et al., 2024).
Microbial Systems
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 (Tarnita et al., 2015, Martinez-Garcia & Tarnita 2016, 2017; Rossine, Martinez-Garcia et al., 2020) and flagellum-repressed Vibrio cholerae (Martinez-Garcia et al., 2018) 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 which 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.
Movement Ecology and Encounter Theory
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. A lot of the ecological theory, from models of species interactions to mathematical epidemiology, assumes that organisms interact with each other following the ‘law of mass action’. This encounter model, although mathematically simple, is incorrect for most real scenarios because it assumes that organisms roam freely in their entire environment and are thus equally likely to interact with any other organism they share the environment with. Our research has provided a new family of encounter models and statistical estimators that relax this well-mixed assumption and account for the patterns of movement behavior observed in animal tracking data (Martinez-Garcia et al., 2020; Noonan et al., 2021). We have shown that these more realistic encounter rates could either be higher or lower relative to mass action and sensitive to the details of the movement behavior, which has profound implications at higher ecological scales as well as in determining the rate at which animals interact with different landscapes features such as road or power lines. We are currently working on better understanding interaction statistics derived from these encounter models (Garcia de Figueiredo et al., 2024) and embedding them into birth-death population dynamics frameworks (Menezes et al., 2025).
Vegetation Dynamics in Water-Limited Systems.
Drylands are home to approximately 35% of the world’s population and cover about 40% of Earth’s land surface, often in developing countries where the economy and human well-being strongly depend on ecosystem services. Therefore, understanding dryland dynamics and, more specifically, predicting and mitigating their response to ongoing climate change is a critical ecological and socio-economic issue. Around the globe, dryland vegetation often forms regular spatial patterns such as rings, spots, and stripes. Many theoretical studies proposing different pattern-forming mechanisms suggest that pattern shapes indicate proximity to desertification transitions, as plants tend to self-organize into specific spatial configurations to optimize the use of available water and ensure survival (Martinez-Garcia et al., 2023). However, none of these studies has established a direct connection between pattern-forming mechanisms and ecosystem-level consequences when drylands approach desertification transitions. Over the last few years, we have developed a bottom-up approach that combines mathematical modeling, greenhouse experiments, and analysis of field and satellite data to describe vegetation dynamics in drylands (Cabal et al., 2020). We have worked at all relevant scales, from individual plants to the whole ecosystem, aiming to understand how different spatial patterns determine ecosystem resilience. At the plant individual level, our work has revealed the mechanisms that drive below-ground plant competition and how plant-soil feedback mechanistically supports theories about the importance of facilitation across stress gradients (Cabal et al., 2020; Cabal, Maciel & Martinez-Garcia, 2024). This work resolved a long-standing debate about the key drivers of below-ground plant interactions, and you can learn more about these results in this outreach movie. At the ecosystem level, we combined satellite images from Sudan and remotely sensed time series of vegetation biomass and precipitation intensity to test model predictions on how vegetation patterns can anticipate impending desertification dynamics (Veldhuis et al., 2022).