Self-organization and criticality in species-rich metacommunities

The stability and dynamics of complex ecosystems is a longstanding puzzle in ecology. Statistical physics approaches have shown that when the number of interacting species is high, surprisingly general statements can be made about the species abundances. While most of these approaches assume well-mixed ecosystems where diversity is maintained by continuous speciation, natural ecosystems are often composed of many local communities between which individuals migrate. The self-organization in these metacommunities is, however, poorly understood. Here we study metacommunities with migration on two length scales: nearest-neighbor and global coupling. Taking into account competitive interactions and demographic noise, we find that when the number of species is large the species' dynamics operates at a critical point which is dominated by demographic fluctuations. In spatially extended systems this results in fractal abundance patterns. For global coupling we derive a mean field theory that yields analytic expressions for the species abundances. In summary, our study reveals a general self-organization process of species-rich metacommunities with important consequences for pattern formation and diversity in spatially extended ecosystems.