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The network approach towards the analysis of the dynamics of complex systems has been successfully applied in a multitude of studies in the neurosciences and has yielded fascinating insights. With this approach, a complex system is considered to be composed of different constituents which interact with each other. Interaction structures can be compactly represented in interaction networks. In this contribution, we present a brief overview about how interaction networks are derived from multivariate time series, about basic network characteristics, and about challenges associated with this analysis approach.
We consider recent reports on small-world topologies of interaction networks derived from the dynamics of spatially extended systems that are investigated in diverse scientific fields such as neurosciences, geophysics, or meteorology. With numerical simulations that mimic typical experimental situations, we have identified an important constraint when characterizing such networks: indications of a small-world topology can be expected solely due to the spatial sampling of the system along with the commonly used time series analysis based approaches to network characterization.
The stimulation and dominance of potentially harmful phytoplankton taxa at a given locale and time are determined by local environmental conditions as well as by transport to or from neighboring regions. The present study investigated the occurrence of common harmful algal bloom (HAB) taxa within the Southern California Bight, using cross-correlation functions to determine potential dependencies between HAB taxa and environmental factors, and potential links to algal transport via local hydrography and currents. A simulation study, in which Lagrangian particles were released, was used to assess travel times due to advection by prevailing ocean currents in the bight. Our results indicate that transport of some taxa may be an important mechanism for the expansion of their distributions into other regions, which was supported by mean travel times derived from our simulation study and other literature on ocean currents in the Southern California Bight. In other cases, however, phytoplankton dynamics were rather linked to local environmental conditions, including coastal upwelling events. Overall, our study shows that complex current patterns in the Southern California Bight may contribute significantly to the formation and expansion of HABs in addition to local environmental factors determining the spatiotemporal dynamics of phytoplankton blooms.