Reconstructing large networks with time-varying interactions.

Reconstructing interactions from observational data is a critical need for investigating natural biological networks, wherein network dimensionality (i.e. number of interacting components) is usually high and interactions are time-varying. These pose a challenge to existing methods that can quantify only small interaction networks or assume static interactions under steady state. Here, we proposed a novel approach to reconstruct high-dimensional, time-varying interaction networks using empirical time series. This method, named "multiview distance regularized S-map", generalized the state space reconstruction to accommodate high dimensionality and overcome difficulties in quantifying massive interactions with limited data. When we evaluated this method using the time series generated from a large theoretical model involving hundreds of interacting species, estimated interaction strengths were in good agreement with theoretical expectations. As a result, reconstructed networks preserved important topological properties, such as centrality, strength distribution and derived stability measures. Moreover, our method effectively forecasted the dynamic behavior of network nodes. Applying this method to a natural bacterial community helped identify keystone species from the interaction network and revealed the mechanisms governing the dynamical stability of bacterial community. Our method overcame the challenge of high dimensionality and disentangled complex time-varying interactions in large natural dynamical systems.