Food web's backbones and energy delivery in ecosystems

A food web can be seen as a collection of pathways distributing energy to the ecological community. Because of thermodynamical as well as ecological constraints, some pathways are more important than others, as they carry a much larger share of the energy flow. Such pathways, composed of ‘strong’ links, might be hidden in the tangled network of trophic interactions. Due to thermodynamic efficiency, leading to considerable loss at every passage, we expect these important pathways to be short – i.e. of minimal length. Minimum length spanning trees, which are trees formed by the minimum number of links to keep food webs connected, have been indicated as main energy routes. To test this hypothesis, we analyzed 30 well-resolved, weighted empirical food webs. From each food web, we extracted the minimum length spanning tree (MLST), and compared it to the maximum weight spanning tree (MWST) – a tree composed of connections of maximum strength. To have a robust comparison, we also computed the minimum weight spanning tree (MinWST), composed of the links of minimal strength. Finally, we extracted from each web 1000 random weighted spanning trees (RWSTs) to serve as a null model. We contrasted the different tree structures, and found that MWSTs are significantly shorter than random trees and MinWSTs, but always longer than MLSTs. In addition, MinWSTs are significantly longer than what expected from random trees. Our results show that in food webs, the bulk of energy travels along pathways that tend to be short, although they never coincide with the minimum length spanning trees.