Food Network and “Real-World” Network Structure
https://www.ncbi.nlm.nih.gov/pubmed/12235364
“Food-web structure and network theory: The role of connectance and size” by Dunne, Williams, and Martinez examines the magnitude of the clustering coefficient and path length in food webs. They mention that while an artificially connected network can have low inter-connections between nodes, real-world networks tend to have high connectance. They refer to the concept of six degrees of separation, which we discussed in class, to argue that in order for the maximum path length between any two people in the world to be within six, the connectance, and therefore clustering coefficient, of the world’s population network must be very high. They go onto discuss how food networks behave the same way: They’re highly connected. This may be counterintuitive, as food networks are directed graphs, and therefore it appears as though one species just eats another species that, in turn, eats another species etc. In fact, it turns out that many preys of one predator often exhibit predator-prey interactions as well, leading to a high clustering coefficient in the network.
Furthermore, the authors of the article describe how food networks behave like “real-world” networks in terms of path length as well: Introducing N species to the network results in an average path length of log(N) between any two nodes. This type of network structure is found in tree-structured data. The log(N) path size, in fact, makes sense, as in a food network, there are much more prey than predators. Each species has a variety of prey they can consume, yet generally, only a few predators that consume it. As a result, in the top of the food network, we can find very minimal species. Yet, at the bottom of the food network, we can find a much wider range of species, mostly plants. Due to this widening characteristic as we go down the food network, we can see how the food network resembles a tree-like structure, and as a result, why it exhibits a log(N) path size.
The properties of the food network relate to the concepts of clustering coefficient and path length that we’ve discussed in class. The fact that food networks exhibit both a high clustering coefficient and a low-ish path size portrays how many “real-world” networks exhibit the same network structure: A lot of node intertwining, yet a clear power bias towards a few nodes.