Fig 1.
Presentation of the data set and its multidimensional nature.
(A) Community data represented as a three-dimensional tensor. Each pixel represents the abundance level (relative to the average abundance of each species in the survey) of the fish species in the North Sea in its 3 dimensions: species, time and space. (B) Map of the study area showing the 7 predefined areas (called roundfish areas) which serve as the spatial scale of our study.
Fig 2.
Results of the principal tensor analysis with 4 principal tensors (PT) explaining together 43% of the total variability in the North Sea fish assemblage.
(A) PT1 showed a spatial gradient in species abundance from North to South. (B) PT2 showed the difference in abundance between strongly localized species (either in the North or the South) and species living in the central part of the North Sea. (C) PT3 showed the abundance difference between species in the West and East of the North Sea. (D) PT4 showed a temporal trend in species abundance.
Table 1.
Correlation analysis to identify environmental influences on spatio-temporal community patterns.
Fig 3.
Classification of fish species based on their spatio-temporal dynamics.
(A) Dendrogram of the Hierarchical Agglomerative Clustering and the separation of 6 clusters. (B-D) Clusters represented on the different principal tensors (PTs), with x-axis showing PT1 projections, and y-axis showing (B) PT2, (C) PT3 and (D) PT4 projections.
Fig 4.
Main characterization of the sub-communities.
(A) Spatio-temporal abundance, represented in a heatmap with time on the x-axis and space on the y-axis. (B) Spatially average abundance of the clusters in the roundfish areas. (C) Temporal average of the abundance per cluster. (D) Illustrations of fish species with the highest abundance in the respective cluster (images from FAO and Wikimedia).
Fig 5.
Biological characteristics (A: maximum length, B: trophic level and C: biogeography) of the spatio-temporal clusters. Widths of the boxplot (A-B) and the bars (C) are proportional to the number of species per cluster.