What makes a motif: The signature of stability selection in food webs
Food web structure can be characterized by the particular frequencies of subgraphs found within them. Although there are thirteen possible configurations of three species subgraphs, some are consistently over-represented in empirical food webs. This is a robust pattern that is found across marine, freshwater, and terrestrial environments. The preferential elimination of unstable subgraphs during the development of the food web can explain the observed pattern. It follows from this simple hypothesis that there should be differences in the stability of different subgraphs, and that stability should be positively correlated to their frequency in food webs. Using 50 food webs collected from a variety of databases I determined the frequency of each of the thirteen possible subgraphs with respect to randomized webs. Then by numerical simulation I determined the quasi sign stability (QSS) of each subgraph.
Of the thirteen subgraphs three are more frequently observed than expected by chance: the tritrophic chain, apparent competition, and direct competition. These three subgraphs are also the most likely to be stable (highest QSS). Those subgraphs that are observed less frequently than expected by chance are also those that are less likely to be stable (low QSS). The link between stability and frequency in empirical food webs is a signature that the loss of unstable configurations results in observed motifs.