Community ecology in 3D: Tensor decomposition reveals spatio-temporal dynamics of large ecological communities

Understanding spatio- temporaldynamics of biotic communities containing large numbers of species is crucial to guide ecosystem managementand conservation efforts. However, traditional approaches usually focus on studying community dynamics either in space or in time, often failing to fully account for interlinked spatio- temporalchanges. In this study, we demonstrate and promote the use of tensor decomposition for disentangling spatio- temporalcommunity dynamics in long-term monitoring data. Tensor decomposition builds on traditional multivariate statistics (e.g. Principal Component Analysis) but extends it to multiple dimensions. This extension allows for the synchronized study of multiple ecological variables measured repeatedly in time and space. We applied this comprehensive approach to explore the spatio- temporaldynamics of 65 demersal fishspecies in the North Sea, a marine ecosystem strongly altered by human activities and climate change. Our case study demonstrates how tensor decomposition can successfully (i) characterize the main spatio- temporalpatterns and trends in species abundances, (ii) identify sub-communities of species that share similar spatial distribution and temporaldynamics, and (iii) reveal external drivers of change. Our results revealed a strong spatial structure in fish assemblages persistent over time and linked to differences in depth, primary production and seasonality. Furthermore, we simultaneously characterized important temporaldistribution changes related to the low frequency temperature variability inherent in the Atlantic Multidecadal Oscillation. Finally, we identified six major sub-communities composed of species sharing similar spatial distribution patterns and temporaldynamics. Our case study demonstrates the application and benefits of using tensor decomposition for studying complex community data sets usually derived from large-scale monitoring programs.