An important problem across many scientific fields is the identification of causal effects from observational data alone. Recent methods (convergent cross mapping, CCM) have made substantial progress on this problem by applying the idea of nonlinear attractor reconstruction to time series data. Here, we expand upon the technique of CCM by explicitly considering time lags. Applying this extended method to representative examples (model simulations, a laboratory predator-prey experiment, temperature and greenhouse gas reconstructions from the Vostok ice core, and long-term ecological time series collected in the Southern California Bight), we demonstrate the ability to identify different time-delayed interactions, distinguish between synchrony induced by strong unidirectional-forcing and true bidirectional causality, and resolve transitive causal chains.

Networks with a modular structure are expected to have a lower risk of global failure. However, this theoretical result has remained untested until now. We used an experimental microarthropod metapopulation to test the effect of modularity on the response to perturbation. We perturbed one local population and measured the spread of the impact of this perturbation, both within and between modules. Our results show the buffering capacity of modular networks. To assess the generality of our findings, we then analyzed a dynamical model of our system. We show that in the absence of perturbations, modularity is negatively correlated with metapopulation size. However, even when a small local perturbation occurs, this negative effect is offset by a buffering effect that protects the majority of the nodes from the perturbation.

We explore the relationship between network structure and dynamics by relating the topology of spatial networks with its underlying metapopulation abundance. Metapopulation abundance is largely affected by the architecture of the spatial network, although this effect depends on demographic parameters here represented by the extinction-to-colonization ratio (e/c). Thus, for moderate to large e/c-values, regional abundance grows with the heterogeneity of the network, with uniform or random networks having the lowest regional abundances, and scale-free networks having the largest abundance. However, the ranking is reversed for low extinction probabilities, with heterogeneous networks showing the lowest relative abundance. We further explore the mechanisms underlying such results by relating a node's incidence (average number of time steps the node is occupied) with its degree, and with the average degree of the nodes it interacts with. These results demonstrate the importance of spatial network structure to understanding metapopulation abundance, and serve to determine under what circumstances information on network structure should be complemented with information on the species life-history traits to understand persistence in heterogeneous environments.