Topological network inference: Understanding ecological communities

Background/Question/Methods
The ability of networks to holistically describe ecological systems and their dynamics has proven useful to community ecology as well as its applications to conservation biology and political ecology. However, analyses of networks have historically entailed correlating theoretical properties with ecological ones, such as the relationship between complexity and stability. While conceptually informative, such approaches have a limited ability to mechanistically account for these relationships and only a superficial means by which to compare networks. In light of this, a flow algorithm was developed to map networks analogous to the spreading of water along interactions resulting in accumulation within species. Compared to singular, often static metrics this technique allows for indirect interactions and network dynamics to be captured. That is, through the distributions of accumulated flow at nodes, networks of varying size and constitution can be directly and quantitatively compared addressing the relationship between a system’s structure and its emergent ecological properties. Moreover, systems can be compared to themselves allowing for questions of complexity, scale-dependence, and thresholds to be addressed more robustly by quantifying the structural differences underlying changes in a system over time.

Results/Conclusions
Testing on both randomly generated Erdös-Rényi networks and empirically determined ecological ones indicated the algorithm is well behaved. The more similar two networks were, the better the mapping between them. Moreover, the “distance” between them approached zero the more similar they were. By removing nodes and comparing systems to themselves we were repeatedly able to demonstrate subadditivity in trophic networks, despite its dismissal in traditional community ecology theory. Additionally, broad-scale comparisons between ecological systems showed clustering, allowing for a new classification scheme to be developed. While still in its infancy, this technique allows the ecological importance of a system’s structure to be approached more mechanistically, enabling more meaningful comparisons between systems.