Dynamics of Complex Living Systems

We are an interdisciplinary research group at the intersection of biology, mathematics, physics, environmental and computer sciences. We are interested in understanding the diversity of patterns and behaviors exhibited by complex living systems across multiple scales, from microbial communities and cell cultures to animal populations and vegetation landscapes. In all these systems, we study how individuals (cells, animals, plants…) interact among them and with the environment and how the outcomes of those interactions propagate to higher levels of organization with cascading effects on the population, community, and ecosystem level. We combine different data types with theoretical models and use the latter to make predictions that can be validated with additional data. Therefore, we often work closely with experimentalists through an international network of collaborators.

We work in two complementary directions to understand the causes and consequences of self-organized emergent patterns in ecology. On the one hand, we develop theory-driven projects to test potential self-organizing principles and formalize them using statistical physics, nonlinear dynamical systems, and complex-systems methods. On the other hand, we investigate various specific systems to test whether these possible self-organizing principles can operate in nature. We choose these systems on multiple scales, from microbial communities to kilometric landscapes, and analyze them combining mathematical modeling and numerous forms of empirical data, seeking to understand to which extent self-organizing principles overlap across different systems and scales.

Dr Ricardo Martínez-García

CASUS Young Investigator Group Leader

Contact

r.martinez-garcia@hzdr.de

+49 3581 375 23 105

Center for Advanced Systems Understanding

Conrad-Schiedt-Straße 20

D-02826 Görlitz

Spatial mathematical ecology

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

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.

Vegetation dynamics in water-limited ecosystems

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).

Animal movement and encounter theory

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.

Publications

The structure of inter-reaction times in reaction-diffusion processes and consequences for counting statistics

Benjamin Garcia de Figueiredo, Justin M Calabrese, William F Fagan, Ricardo Martinez-Garcia - arXiv preprint arXiv:2409.11433

Many natural phenomena are quantified by counts of observable events, from the annihilation of quasiparticles in a lattice to predator-prey encounters on a landscape to spikes in a neural network. These events are triggered at random intervals when an underlying dynamical system occupies a set of reactive states in its phase space. We derive a general expression for the distribution of times between events in such counting processes assuming the underlying triggering dynamics is a stochastic process that converges to a stationary distribution. Our results contribute to resolving a long-standing dichotomy in the study of reaction-diffusion processes, showing the inter-reaction point process interpolates between a reaction- and a diffusion-limited regime. At low reaction rates, the inter-reaction process is Poisson with a rate depending on stationary properties of the event-triggering stochastic process. At high reaction rates, inter-reaction times are dominated by the hitting times to the reactive states. To further illustrate the power of this approach we apply our framework to obtain the counting statistics of two counting processes appearing in several biophysical scenarios. First, we study the common situation of estimating an animal’s activity level by how often it crosses a detector, showing that the mean number of crossing events can decrease monotonically with the hitting rate, a seemingly ‘paradoxical’ result that could possibly lead to misinterpretation of experimental count data. Second, we derive the ensemble statistics for the detection of many particles, recovering and generalizing known results in the biophysics of chemosensation. Overall, we …

Plant antagonistic facilitation across environmental gradients: a soil-resource ecosystem engineering model

Ciro Cabal, Gabriel A. Maciel, Ricardo Martinez-Garcia - New Phytologist 244, 670-682

Theory questions the persistence of nonreciprocal interactions in which one plant has a positive net effect on a neighbor that, in return, has a negative net impact on its benefactor – a phenomenon known as antagonistic facilitation. We develop a spatially explicit consumer‐resource model for belowground plant competition between ecosystem engineers, plants able to mine resources and make them available for any other plant in the community, and exploiters. We use the model to determine in what environmental conditions antagonistic facilitation via soil‐resource engineering emerges as an optimal strategy.
Antagonistic facilitation emerges in stressful environments where ecosystem engineers’ self‐benefits from mining resources outweigh the competition with opportunistic neighbors. Among all potential causes of stress considered in the model, the key environmental parameter driving changes in the …

Shear and transport in a flow environment determine spatial patterns and population dynamics in a model of nonlocal ecological competition

Nathan O Silvano, João Valeriano, Emilio Hernández-García, Cristóbal López, Ricardo Martinez-Garcia - arXiv preprint arXiv:2409.04268

Populations very often self-organize into regular spatial patterns with important ecological and evolutionary consequences. Yet, most existing models neglect the effect that external biophysical drivers might have both on pattern formation and the spatiotemporal population dynamics once patterns form. Here, we investigate the effect of environmental flows on pattern formation and population dynamics using a spatially nonlocal logistic model (or Fisher-Kolmogorov equation) coupled to a simple shear and a Rankine vortex flow. We find that, whereas population abundance generally decreases with increasing flow intensity, the effect of the flow on the pattern instability depends on the spatial structure of the flow velocity field. This result shows that the velocity field interacts with the spatial feedbacks responsible for pattern formation in non-trivial ways, leading to a variety of spatiotemporal population dynamics regimes in which the total population abundance can exhibit either regular oscillations with a characteristic frequency or more erratic dynamics without a well-defined period. More generally, the diversity of spatiotemporal population dynamics caused by the interplay between self-organizing feedbacks and environmental flows highlights the importance of incorporating environmental and biophysical processes when studying both ecological pattern formation and its consequences.