Looking locally to see globally: Motif sampling to distinguish interaction type and predict dynamical properties of whole networks
Network motifs are the building blocks of complex networks, and their analysis has found application in several branches of biology, including ecology. Bipartite networks of ecological interactions can be broadly subdivided according to the type of interaction they describe. For example, into those representing mutualisms (e.g., plant-pollinator) and those modelling antagonisms (e.g., plant-herbivore). Here we posit that different types of ecological interactions leave distinctive signatures on network structure, such that we can distinguish between mutualistic and antagonistic networks by profiling their motifs.
We find that motifs can be used to identify the types of interactions in ecological networks. For example, antagonistic networks have significantly fewer short cycles than expected at random, while short cycles are over-represented in mutualistic networks. This makes ecological sense, as small cycles represent competition for shared resources in bipartite antagonistic networks; this result is also consistent with previous findings, given that nested networks (such as mutualistic ones) should be enriched in small cycles. Our findings also have important dynamical consequences, given that motifs strongly influence spectral properties of the system, such as the sign and magnitude of the leading eigenvalue of the corresponding community matrix---which determines dynamical stability.
Empirically describing an ecological network in its entirety is notoriously difficult---one can never be sure they have detected every last interaction. Methods based on sampling small sub-networks, such as motifs analysis, get around this problem by reliably approximating overall network properties even when only part of the network is described. Thus, our findings help provide greater confidence in our ability to describe natural systems even when our data are incomplete.