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The Barents Sea is a shelf break sea (1.6 mill. km², average depth: 230 m), located north of Norway and Russia (Supplementary Fig. 1). Since 2004, a joint ecosystem survey with Norwegian and Russian research vessels has covered the Barents Sea in summer–early autumn, during minimum ice coverage. Stations were allocated on a standardized grid (35 nautical miles between stations). At each station a demersal trawl (Campelen 1800) was towed for 15 min at 3 knots (0.75 nautical miles ~1,400 m). The catch was sorted (identified to lowest possible taxonomic level), counted and weighed. Environmental information was sampled with a conductivity–temperature–depth (CTD) profiler at most stations. Sea-ice data were obtained from SSM/I passive microwave remote sensing from the National Snow and Ice Data Center³¹ (http://www.nsidc.org). Ice presence was calculated as number of days with ice present during each year.

The annual cycle of temperature along the Kola section and the sea-ice coverage in the Barents Sea are shown in Supplementary Fig. 2. The Kola section, 0–200 m depth layer, represents a proxy for the temperature development of the Barents Sea (Supplementary Fig. 2a), and the first decade of the 21st century was the warmest ever recorded³² (since the start of the survey in 1900). The duration of the ice-free season increased through the study period (Supplementary Fig. 2b). The timing of the survey was consistent through the study period 2004–2012, with only a week’s delay in later years (and an expanded survey period in 2010).

To calculate yearly averages in Barents Sea bottom-water temperature, and relative areas covered by different water masses (Atlantic Water, T < 2 °C; mixed-water masses, 0 °C < T < 2 °C; Arctic Water, T < 0 °C) and sea ice, the environmental data were first spatially interpolated on a regular grid (grid size, 50 × 50 km) by Kriging³³, and the yearly estimates (Supplementary Fig. 3) were based on the gridded data to avoid sampling bias and facilitate between year comparisons.

More than 220 fish species are known to occur in the Barents Sea, and approximately 100 fish species are regularly caught on the ecosystem surveys. However, owing to a changing taxonomic identification protocol, several species were merged on a higher taxonomic level. A further species reduction due to very low occurrence (one station only) and removal of pelagic species left us with 74 taxonomic groups identified similarly throughout the study period (Supplementary Table 1). The catches in the survey trawl were standardized to a given tow distance (1 nautical mile). From 2004 to 2012 the ecosystem surveys sampled 4,463 bottom trawl stations—of these 3,940 were included in our analyses. Stations were removed because they were repeated successively (572—for example, diurnal stations), were of low quality (96—for example, trawl hauls mostly containing mud), had tow time less than 10 min (64—unrepresentative sampling) or more than 60 min (11—various test stations), or were sampled on unrepresentative depths (54 less than 50 m and 287 more than 500 m). Following the removal of pelagic species, some stations were left empty or with an occurrence of only one species (monostations). These 11 stations were removed, leaving 3,940 stations for our analyses.

To classify the different fish communities in the Barents Sea in 2004 (start of ecosystem survey), we performed a cluster analysis (based on Bray–Curtis dissimilarities and Ward linkage). Visual inspection of the dendrogram revealed three well-separated clusters (that is, fish communities), as shown by the large interval of Bray–Curtis dissimilarity between the splits into two, three and four clusters³⁴ (Supplementary Fig. 6a), and by the clear separation of the clusters when plotted onto an ordination diagram³⁵. The species abundance profile of each fish community was calculated by averaging individual species abundances across stations classified to that community in 2004 (Supplementary Fig. 5). The different stations were mapped with colour coding denoting cluster affiliation (Supplementary Fig. 6b). The Barents Sea open waters clearly comprise three distinct fish communities (here called Atlantic, Central and Arctic), with a spatial pattern suggesting that community structure is influenced by water masses and habitat characteristics (Supplementary Fig. 4).

The Atlantic community comprises two different sub-communities (shallow Atlantic and deep Atlantic) that are related to different depth habitats. In the figures, the two Atlantic sub-communities are identified by using different symbols (Figs 1c, d and 2 and Supplementary Figs 7,11 and 12) or colours (Supplementary Figs 5,6,8 and 10), and are treated separately when assessing distributional shifts and changes in areal coverage because of the expected differences in response to climate warming of deep versus shallow fish communities. A discriminant analysis was applied to reveal which species contribute most to the separation of the clusters (Supplementary Fig. 6c), and the resulting discriminant functions were used to classify fish communities sampled over the study period. The similarities of the two maps show the predictive capability of the discriminant function (Supplementary Fig. 6b, d). Mapping the classified stations in the Barents Sea allowed us to track changes in distribution of the Atlantic, Central and Arctic communities (Fig. 1c, d and Supplementary Fig. 7).

Estimates of areal coverage and position of community distributions are biased by sampling effort and distribution, which vary between years. To overcome sampling bias we gridded the data (Supplementary Fig. 8). The grid size was 50 × 50 km (~27 nautical miles), ensuring approximately one station per grid cell. The grid cells were then classified according to the community affiliations of the stations found in the cells. Cells missing stations were assigned the community from the closest nearby station (Supplementary Fig. 8). This approach yields a conservative assignment when stations are missing in the margin of the surveyed area. To investigate possible changes in community distribution through time with regard to position (geographical shift) and areal coverage (expanding or retracting), for each community we calculated the centre of distribution (weighted average longitude and latitude) and the proportion of area covered relative to the total area considered, based on the gridded data (Fig. 2). Temporal trends in community area coverage were estimated by linear regression, fitting general linear models, and F-tests were used to evaluate trends’ significance (Supplementary Table 2).

We also assessed community affinity to environmental characteristics such as bottom depth, water temperature and ice presence (Supplementary Fig. 9 and Supplementary Table 3). Affinities to environmental conditions were addressed using binomial generalized linear models (GLMs; Supplementary Fig. 10 and Supplementary Table 4). For each community, the GLMs were estimated based on the presence–absence data and on the environmental conditions at each station, an approach akin to species distribution modelling³⁶, but here applied to the distribution of communities rather than individual species. The models’ output allowed us to characterize affinities (in 2004 and for all years). The environmental variables included as predictors in the GLMs showed some degree of collinearity, but even the strongest correlation detected (r = −0.31, between water temperature and ice presence in 2004) had an absolute value far below |r| = 0.7, which is considered a threshold level beyond which collinearity may seriously distort model estimation³⁷. Another problem afflicting models of distributional data is spatial autocorrelation, which may lead to overly optimistic standard error estimates^{36, 38}. This is primarily a concern for predictive modelling purposes, which are not a goal of this study. In our data, inspection of correlograms of the binary response variables showed significant positive correlation for lag distances of up to about 300 km, but the positive autocorrelation was effectively reduced in correlograms of the GLMs residuals, indicating that the environmental predictor variables could account for most of the spatial autocorrelation in the response. The latter implies that spatial autocorrelation should not be a concern in our GLMs (ref. 38).

To investigate the change in abundance of individual fish species within the specified Arctic area (Fig. 3 inset map), the abundances in 2004 were subtracted from those of each year in the period 2005–2012. The abundance deviations were plotted by sorting species according to their geographic affinity (average latitude of a species distribution, all years), from south to north (Fig. 3).