Looking at biological communities with 3D lenses.
Understanding the spatio-temporal dynamics of biotic communities (i.e. knowing when and where different species are) is crucial for the management and conservation of ecosystems. We promote the use of an advanced statistical method, called ‘tensor decomposition’, to reveal the spatio-temporal dynamics of species assemblages using the multidimensionality of collected data set (see study by Frelat et al. 2017).
How many fish are in the ocean? Answering this question is not easy, however scientists have developed different sampling strategies to help estimate the fish density. The most common sampling is performed by fishing with a net -according to a standard protocol-, and by counting, and identifying the species’ names of all the catches. When the exact same procedure is repeated across a large area for decades it is then possible to estimate the distribution and the dynamics of fish species. We argue that this data set, called ‘community data’, can be represented as a three-dimensional tensor (or array, in a 3D cuboid shape), with one dimension being the species’ name, a second the areas covered, and a third that considers time (Fig. 1A).
Traditionally, most of the statistics and numerical models developed to study community data have focused on matrices which are two-dimensional (rows and columns) (see Legendre & Legendre 2012, for an introduction to data analysis for ecologists). However, the simplification of the 3D community data into a flat-view 2D matrix results in the loss of information. Accordingly, since the late 1960s, mathematicians have developed tools to analyse data sets with more than two dimensions; these methods are generally called ‘tensor decomposition’ (for a recent review see Cichocki et al. 2015). Tensor decomposition is commonly used for data mining in large data sets in chemistry, neuroscience, bioinformatics, and other disciplines but not in ecology. We used the North Sea fish community as a case study to demonstrate the applicability and benefits of tensor decomposition in ecology.
The North Sea fish community has been monitored consistently for the past 30 years. Our results revealed a strong spatial structure in fish assemblages, linked with differences in depth (i.e. shallow waters host different fish species than deep waters). We also linked the temporal dynamics of fish to the Atlantic Multidecadal Oscillation –a global climate variability associated with the temperature of the North Atlantic Ocean. Considering the 3D structure of the data set, we could investigate the relation between the spatial distribution AND temporal dynamics, resulting in six sub-communities of species that share similar spatio-temporal patterns (Fig. 1B). Thus, we encourage the use of Tensor decomposition among ecologists and we provide a tutorial, containing script and data, explaining multivariate analysis from traditional 2D approaches to 3D tensor decomposition.
Frelat R, Lindegren M, Denker TS, Floeter J, Fock HO, Sguotti C, et al. (2017) Community ecology in 3D: Tensor decomposition reveals spatio-temporal dynamics of large ecological communities. PLoS ONE 12(11): e0188205. https://doi.org/10.1371/journal.pone.0188205
Legendre P, Legendre LF. Numerical ecology. Vol. 24. Elsevier; 2012. ISBN: 9780444538680
Cichocki A, Mandic D, De Lathauwer L, Zhou G, Zhao Q, Caiafa C, et al. Tensor Decompositions for Signal Processing Applications: From two-way to multiway component analysis. IEEE Signal Process Mag. 2015; 32: 145–163. https://doi.org/10.1109/MSP.2013.2297439