Self-organization and criticality in spatially coupled ecosystems

• Applicant: Dr. Jonas Denk
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics ; Biophysics
• Term: from 2020 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 445916943

Ecological systems fulfill vital roles in all natural domains ranging from soil to the human host. Theoretical and experimental studies have yielded insights into the stability of ecological communities as a function of their interaction structures. Apart from interactions, species undergo demographic fluctuations, which eventually lead to stochastic population extinctions. To balance stochastic extinctions, ecological theories typically assume constant immigration of species from an inexhaustible, static external pool of species. While this assumption has helped to study genetic diversity on islands that are coupled to a mainland with fast relaxation, it is not suitable when dynamics of spatially connected habitats occur on comparable time scales as in many natural spatially extended ecosystems. In this case, immigration of individuals is consistent with their loss on another habitat and migration is a self-organized process of the metacommunity. In particular in the presence of many coexisting competing species, where species abundances can be low and stochastic extinctions are probable, I hypothesize that the details of migration and their role in balancing stochastic extinction play an important role for the community structure. However, the interplay between self-consistent migration, ecological interactions, and demographic fluctuations, and their combined impact on metacommunity assembly is poorly addressed. My overall research goal for the next two years is to develop a mathematically and experimentally well-founded framework to investigate the self-regulation process of spatially coupled ecosystems. I plan to resolve the interplay between interactions, demographic fluctuations and spatial coupling on various lengthscales ranging from scale-free (global), through long-distance, to diffusive dispersal. My preliminary results based on a self-consistent analysis and numeric simulations indicate interesting relations between migration strength and diversity and reveal a self-organization to criticality unprecedented in ecological models with static immigration. The proposed self-consistent analysis forms an ideal basis to analytically address general properties of ecosystems in the presence of global coupling (Aim 1). All my mathematical approaches will be substantiated by laboratory experiments with microbial communities (designed from Escherichia coli strains available in the Hallatschek lab) with spatial couplings on different length scales. In the second stage of my project (Aim 2), I will address short-ranged migration in terms of diffusive dispersal. I plan to investigate universal equilibrium properties of diffusively coupled ecosystems in the context of percolation theory as well as non-equilibrium properties in range expansions in theory and experiments. To address intermediate length scales, I will study long-distance dispersal on variable length scales in theory and experiments based on coarse-grained dispersal kernels (Aim 3).

• DFG Programme: WBP Fellowship
• International Connection: USA
• Host: Professor Dr. Oskar Hallatschek