Local and collective transitions in sparsely-interacting ecological communities

TL;DR

This paper investigates how sparse competitive interactions in ecological communities lead to various structural regimes, including fragmentation and collective transitions, driven solely by changes in interaction strength.

Contribution

It introduces a theoretical model showing how community structure and diversity change with interaction strength, revealing new collective and percolation transitions in sparse networks.

Findings

Communities fragment into small subgraphs at strong interactions.

Weaker interactions lead to larger, more complex community structures.

Two key transitions are identified: percolation and multiple equilibria.

Abstract

Interactions in natural communities can be highly heterogeneous, with any given species interacting appreciably with only some of the others, a situation commonly represented by sparse interaction networks. We study the consequences of sparse competitive interactions, in a theoretical model of a community assembled from a species pool. We find that communities can be in a number of different regimes, depending on the interaction strength. When interactions are strong, the network of coexisting species breaks up into small subgraphs, while for weaker interactions these graphs are larger and more complex, eventually encompassing all species. This process is driven by emergence of new allowed subgraphs as interaction strength decreases, leading to sharp changes in diversity and other community properties, and at weaker interactions to two distinct collective transitions: a percolation transition, and a transition between having a unique equilibrium and having multiple alternative equilibria. Understanding community structure is thus made up of two parts: first, finding which subgraphs are allowed at a given interaction strength, and secondly, a discrete problem of matching these structures over the entire community. In a shift from the focus of many previous theories, these different regimes can be traversed by modifying the interaction strength alone, without need for heterogeneity in either interaction strengths or the number of competitors per species.