Within a complex system, such as a social system or environment, small changes can induce qualitative transformations of the system itself. Such systems are known as tipping elements. When these tipping elements reach a tipping point, they can result in a small, localized perturbation that can cause qualitative changes across the entire system.

Wunderling et al. modeled the moisture recycling network of the Amazon rainforest as a complex network of interacting tipping elements. In this network, an area either had low or high tree cover. The authors examine how motifs, or localized interactions within a region, can result in a domino effect of tipping cascades that affect a system on a macroscale through the process of water transpiration.

“Simple local interaction can relate to the vulnerability of a whole macroscopic system,” said author Benedikt Stumpf.

When a node in the system is tipped, it has an impact on nearby nodes or a target node and an indirect impact on intermediary nodes. The authors compared four different types of motifs, known as the feed forward loop, the secondary feed forward loop, the zero loop and the neighboring loop.

They found that in regions with a high density of motifs, tipping cascades were more likely to occur. Specifically, coupled feed forward loops resulted in a 90% decrease of strength. Tipping cascades such as these can result in the decreased robustness of the moisture recycling networks.

“In the future, we hope to identify more exact tipping thresholds across different regions in the Amazon rainforest. Each region is unique, and by modeling them individually, we expect to fine-tune our results,” said author Nico Wunderling.

Source: “How motifs condition critical thresholds for tipping cascades in complex networks: Linking micro- to macro-scales,” by Nico Wunderling, Benedikt Stumpf, Jonathan Krönke, Arie Staal, Obbe A. Tuinenburg, Ricarda Winkelmann, and Jonathan F. Donges, Chaos (2020). The article can be accessed at https://doi.org/10.1063/1.5142827.