We all know that ecological systems are complex, but only recently has it become clear that many features of complex systems emerge from universal properties of networks. Networks arise whenever interactions take place among a set of objects. This leads us to ask, what insights can network properties and behavior provide about ecological phenomena?

Common features of complex networks include positive and negative feedback loops, criticality, modularity, scale-free patterns, and dual phase evolution. Mathematical models and cellular automata simulations help us to understand these processes in isolation. Individual-based simulations (developed with close reference to empirical data) provide the means to investigate the interplay of these effects in specific scenarios. Integrating these approaches can help ecologists to target relevant parameters in designing empirical studies and develop a stronger understanding of causality in specific systems. In some cases, this strategy allows unprecedented predictive power; in others, it tells us that our predictive ability will be poor no matter how good our data.

Here, we survey recent ecological studies using this integrated modeling approach and show how it has led to a deeper understanding of many ecological problems.

Results/Conclusions

In this review, we show that simulation studies reveal how processes as varied as sea-stars invading coral reefs,  wildfires spreading in eucalypt forest, novel adaptations arising in a species, and the migration of water birds between lakes, can all be modeled as epidemic processes whose behavior depends critically on the connectivity of an underlying network.

Distinct, alternating phases can often be seen in geographic distributions, where fragmented populations display sharply divergent dynamics from those of connected populations. These phase changes are evident at multiple spatial and temporal scales, suggesting a unified explanation for events as diverse as patterns of post-glacial forest migration in Canada, ecotypes and adaptive radiation events on islands and lakes, and punctuated equilibrium in the fossil record. More tentatively, models of this process suggest ways in which robust, modular structures can emerge from a chaotic initial state, bridging the gap between ecosystem-based and neutral theories of ecological self-organization.

The pervasive impact of phase changes in network connectivity provides a general explanation for diverse patterns in ecological dynamics. Understanding how these phase changes interact at different spatial and temporal scales, and their role in the origins of robust complex ecosystems, is a key challenge in current research.