Supplementary material from "Reconstructing ecological networks with noisy dynamics"

Ecosystems functioning is based on an intricate web of interactions among living entities. Most of these interactions are difficult to observe, especially when the diversity of interacting entities is large and they are of small size and abundance. To sidestep this limitation, it has become common to infer the network structure of ecosystems from time series of species abundance, but it is not clear how well can networks be reconstructed, especially in the presence of stochasticity that propagates through ecological networks. We evaluate the effects of intrinsic noise and network topology on the performance of different methods of inferring network structure from time-series data. Analysis of seven different four-species motifs using a stochastic model demonstrates that star-shaped motifs are differentially detected by these methods while rings are differentially constructed. The ability to reconstruct the network is unaffected by the magnitude of stochasticity in the population dynamics. Instead, interaction between the stochastic and deterministic parts of the system determines the path that the whole system takes to equilibrium and shapes the species covariance. We highlight the effects of long transients on the path to equilibrium and suggest a path forward for developing more ecologically sound statistical techniques.