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To build Sentinel2GlobalLULC, we followed two main steps. First, we established a spatio-temporal consensus between 15 global LULC products for 29 LULC classes. Then, we extracted the maximum number of Sentinel-2 RGB images representing each class. Each image is a tile that has 224 × 224 pixels at 10 × 10 m spatial resolution and was built as a cloud-free composite from all the Sentinel-2 images acquired between June 2015 and October 2020. Both tasks were implemented using GEE, an efficient programming, processing and visualisation platform that allowed us to have free manipulation and access to all used LULC products and Sentinel-2 imagery, simultaneously.Finding spatio-temporal agreement across 15 global LULC productsTo establish the spatio-temporal consensus between different LULC products for each one of the 29 LULC classes, we followed four steps: (1)Identification of the LULC products to be used in the consensus, (2)Standardization and harmonization of the LULC legend that was subsequently used to annotate the image tiles, (3)Spatio-temporal aggregation across LULC products, and (4)Spatial reprojection and tile selection based on optimized spatial purity thresholds.Global LULC products selectionThe adopted purity measure for spatio-temporal agreement across the 15 global LULC products we selected from GEE (Table 2) aims to find areas of high consensus to maximize the annotation quality. Spatial and temporal consensus across such rich diversity of LULC products, in terms of spatial resolution, time coverage, satellite source, LULC classes and accuracy, was used as a source of robustness for our subsequent LULC annotation. Products outside GEE were not used due to computing limitations.Table 2 Main characteristics of the 15 global Land-Use and Land-Cover (LULC) products available in Google Earth Engine (GEE) that were combined to find consensus in the global distribution of 29 main LULC classes.Full size tableStandardization and Harmonization of LULC legendsLand cover (LC) data describes the main type of natural ecosystem that occupies an area; either by vegetation types such as shrublands, grasslands and forests, or by other biophysical classes such as permanent snow, bare land and water bodies. Land use (LU) includes the way in which humans modify or exploit an area, such as urban areas or agricultural fields.To build our 29 LULC classes nomenclature, we established a standardization and harmonization approach based on expert knowledge. During this process, we took into account both the needs of different practitioners in the global and regional LULC mapping field and the thematic resolution of the global LULC legends available in GEE. Our nomenclature consists of 23 LC and 6 LU distinct classes identified through specific consensus rules across 15 LULC products (see Table 4). A six-level (L0 to L5) hierarchical structure was adopted in the creation of these 29 LULC classes (Fig. 2). To facilitate the inter-operability of our 29 legends at the finest level L5 across all LULC products and with the widely used FAO’s hierarchical Land Cover Classification System (LCCS)1, we have established an LULC classification system where the 29 classes can be mapped directly to FAO’s LCCS as explained in the table of Supplementary File 1. The LC part in our dataset contains 20 terrestrial ecosystems and 3 aquatic ecosystems. The terrestrial systems are: Barren lands, Grasslands, Permanent snow, Moss and Lichen lands, Close shrublands, Open shrublands, in addition to 12 Forests classes that differed in their tree cover, phenology, and leaf type. The aquatic classes are: Marine water bodies, Continental water bodies, and Wetlands; furthermore, wetlands were divided into 3 classes: Marshlands, Mangroves and Swamps. The LU part is composed of urban areas and 5 coarse cropland types that differed in their irrigation regime and leaf type. In Table 3, you can find the semantic definition of each one of the 29 classes in Sentinel2GlobalLULC. We provided a table in Supplementary File 2, for a more detailed definition of each LULC class.Fig. 2Tree representation of the six-level (L0 to L5) hierarchical structure of the Land-Use and Land-Cover (LULC) classes contained in the Sentinel2GlobalLULC dataset. Outter circular leafs represent the final or most detailed 29 LULC classes (C1 to C29) of level L5. The followed path to define each class is represented through inner ellipses that contain the names of intermediate classes at different levels between the division of the Earth’s surface (square) into LU and LC (level L0) and the final class circle (level L5). All LULC classes belong to three levels at least, except the 12 forest classes that belong to L5 only.Full size imageTable 3 Semantic signification of each one of the 29 Land Use and Land Cover (LULC) classes contained in the Sentinel2GlobalLULC dataset according to the six-level (L0 to L5) hierarchical structure.Full size tableCombining products across time and spaceFor each one of the 29 LULC classes, we combined in space and time the global LULC information among the 15 GEE LULC products. This way, each image was annotated with a LULC class only if all combined products agreed in its corresponding tile (i.e., 100% of agreement in space and time). For each product and LULC type, we first set one or more criteria to create a global mask at the native resolution of the product in which each pixel was classified as 1 or 0 depending on whether it met the criteria for belonging to that LULC type or not, respectively (see first stage in Table 4). For certain LULC classes, some products did not provide any relevant information, so they were not used. For example (Table 4), in Grasslands (C3), Open Shrublands (C4) and Close Shrublands (C5), we combined 14 products, while in UrbanBlUpArea (C29) and Permanent Snow (C23) we only combined 10 and 7 products, respectively.Table 4 First stage of the rule set criteria used to find consensus across the 15 Land-Use and Land-Cover (LULC) products available in Google Earth Engine (GEE) for each of the 29 LULC classes contained in the Sentinel2GlobalLULC dataset.Full size tableThen (see second stage in Table 5), for each LULC type, we calculated the average of all the masks obtained from each product to create a final global probability map from all products with values ranging between 0 and 1. Value 1 meant that all products agreed to assign that pixel to a particular LULC class, while 0 meant that none of the products assigned it to that particular class (Fig. 3). These 0-to-1 values are interpreted as the spatio-temporal purity level of each pixel to belong to a particular LULC class and are provided as metadata with each image.Table 5 Second stage of the rule set criteria used to find consensus across the 15 Land-Use and Land-Cover (LULC) products available in Google Earth Engine (GEE) for each of the 29 LULC classes contained in the Sentinel2GlobalLULC dataset.Full size tableFig. 3Example of the process of building the final global probability map for one of the 29 Land-Use and Land-Cover (LULC) classes (e.g. C1: “Barren”) by means of spatio-temporal agreement of the 15 LULC products available in Google Earth Engine (GEE). The final map is normalized to values between 0 (white, i.e., areas with no presence of C1 in any product) and 1 (black spots, i.e., areas containing or compatible with the presence of C1 in all 15 products), whereas the shades of grey corresponds to the values in between (i.e., areas that did not contain or were not compatible with the presence of C1 in some of the products). This process is divided into two stages: the first stage (the blue part, see details in Table 4) and the second stage (the yellow part, see details in Table 5). LULC products available for several years are represented with superposed rectangles, while single year products are represented with single rectangles. GMP: global probability map, NA: Not Available.Full size imageAs an example of the first stage (see details in Table 4), to specify if a given pixel belongs to Dense Evergreen Needleleaf Forest, we evaluated its tree cover level using “ ≤ “ and “ ≥ “, while for bands containing the leaf type information, we used the equal operator “ = “. For the spatio-temporal combination of multiple criteria we have used the following operators: “AND”,“OR” and “ADD”. For example, we combined the tree cover percentage criteria with the leaf type criteria using “AND” to select forest pixels that met both conditions. To combine many years instances of the same product, we used “ADD”, except for product P13, where we used “AND” to identify permanent water areas only. Whenever we used the “ADD” operator, we normalized pixel values afterwards to bring it back to a probability interval between 0 and 1 using the division by the total number of combined years or criteria.In the second stage (see details in Table 5), we combined for each LULC class the 15 global probability maps previously derived from each product to create a final global probability map (Fig. 3). This combination was carried out using various operators such as “ADD”, “MULTIPLY” and “OR”, depending on the LULC type. When “ADD” was used, the final pixel values were normalized by dividing the final addition value of each pixel by the total number of added products. The “MULTIPLY” operator was mostly used at the end, to remove urban areas from non-urban LULC classes, or to remove water from non-water LULCs. The multiplication operator was also adopted to make sure that a certain criteria was respected in the final probability map. For instance, for the swamp class, we multiplied all pixels in the final stage by a water mask where saline water areas have a value of 0 in order to eliminate mangrove from swamp pixels and vice versa. Finally, we used “OR” operator between different water related products to take advantage of the fact that they complement each other in terms of spatial-temporal coverage and accuracy.In GEE, when two products are aggregated using “ADD”, “MULTIPLY” or any other operator, the output is aggregated at the spatial resolution of the product at the left of the operator. Hence, to maintain the finest spatial resolution in the final probability map, we multiplied everything by product P15 and placed it at the left of the final “MULTIPLY” operation (See Table 5). Hence, all the 29 final probability maps were generated at the P15 spatial resolution of 30 m/pixel (except the urban class C29 which maintained the 30 m/pixel resolution of product P14).Re-projection and Selection of purity thresholdSince our objective was finding pure Sentinel-2 image tiles of 224 × 224 10-m pixels representing each LULC class, we reprojected the 30 m/pixel probability maps to 2240 m/pixel using the spatial mean reducer in GEE. That is, each pixel value at 2240 m resolution was computed using the mean over all the 30m-pixel values contained within it. Hence, the resulting pixel values at 2240 m resolution represent the purity level that each Sentinel-2 image tile of 224 × 224 10-m pixels has. We illustrated the reprojection and selection processes in Fig. 4.Fig. 4Example of the workflow to obtain a Sentinel-2 image tile of 2240 × 2240 m for one of the 29 Land-Use and Land-Cover (LULC) classes (e.g. C1: “Barren”). The process starts with the reprojected final global probability map obtained from stage two (Table 5) and ends with its exportation to the repository of a Sentinel-2 image tile of 224 × 224 pixels. The white rectangle is the only one having a probability value of 1 (Recall that the purity threshold used for Barren was 1, i.e., 100%). The black pixels has a null probability value, while the probability values between 0 and 1 are represented in gray scale levels.Full size imageFor each one of the reprojected maps, we defined a pixel value threshold to decide whether a given 2240 × 2240 m tile was representative of each LULC class or not. Since training DL image classification models needs a large number of high quality (both in terms of image quality and annotation quality) image tiles to reach a good accuracy, when the spatial purity of 100% (full agreement across products in all the pixels of the 224 × 224 tile) resulted in a small number of agreement tiles for a particular class, the purity threshold was decreased for that class until the number of tiles was larger than 1000 or further decreased in less abundant classes to a minimum of 75% of purity. The found purity value is always provided as metadata for each image in the dataset, so the user can always restrict its analysis to those image tiles and classes at any desired purity level. Decreasing the purity threshold down to 75% for the less abundant classes (e.g swamp, mangrove, etc.) was a trade-off between maintaining a good data annotation quality and providing a sufficient number of tiles in each class. In Table 6, we present the number of agreement tiles found at different purity thresholds ranging from 75% to 100% for each LULC class. This spatial purity was not further decreased since machine learning image classification models are known to be robust when the target class is spatially dominant in each training image (it occupies more than 60% of the pixels in the scene)42. On the other hand, when the number of pure tiles for a LULC class was too large to be downloaded (i.e., greater than 14000), we applied a selection algorithm as described in the Supplementary File 3, to download a maximum of 14000 spatially representative images. For this, the world was divided into a one-degree squared cell grid. If a cell contained less than 50 image tiles, we selected them all. If it contained more than 50, we applied that automatic maximum geographic distance algorithm that selected images as far from each other as possible in a number proportional to the number of existing images in that cell. The map in Fig. 6 shows the global distribution of the selected 194877 image tiles contained in Sentinel2GlobalLULC and distributed in 29 LULC classes.Table 6 Summary of the varying number of found and eventually selected Sentinel-2 image tiles of 224 × 224 pixels depending on the different consensus level reached across the 15 Land-Use and Land-Cover (LULC) products available in Google Earth Engine (GEE) for each of the 29 LULC classes contained in the Sentinel2GlobalLULC dataset.Full size tableData extractionSentinel2GlobalLULC provides the user with two types of data: Sentinel-2 RGB images (jpeg and geotif versions) and CSV files with associated metadata. In the following subsections, we describe the process for associating metadata, including the Global Human Modification (GHM) index.Global human modification index extractionAs an additional metadata related to the level of human influence in each image, we calculated for each tile in GEE, the spatial mean of the global human modification index for terrestrial lands43, where 0 means no human modification and 1 means complete transformation. Since the original GHM product was mapped at 1 × 1 km resolution, we reprojected it to 2240 × 2240 m using the same reprojection procedure explained in (Re-projection and Selection of purity threshold).CSV files generationOnce the tiles were selected, for each LULC class we listed the image tiles in descendent order of purity. Metadata included: geographical coordinates of each tile centroid, tile purity value, name and ID of the LULC class, and average GHM index for that tile. Then, we used the geographical coordinates of each tile to identify its exact administrative address geolocation. To implement this reverse geo-referencing operation, we used a free request-unlimited python module called reverse_geocoder. This way, we assigned a country code, two levels of administrative departments, and the locality to each tile.For LULC classes that had more than 14000 pure tiles, we have released the coordinates before and after the distance-based selection in case the user wants to download more tiles or use our consensus coordinates for other purposes.Sentinel-2 RGB images exportationAfter extracting all these pieces of information and grouping them into CSV files, we went back to the geographic center coordinates of each tile and used them to extract the corresponding 224 × 224 Sentinel-2 RGB tiles using GEE. Each exported image was identical to the 2240 × 2240 m area covered by its Sentinel-2 tile.We chose “Sentinel-2 MSI (Multi-Spectral Instrument) product” since it is free and publicly available in GEE at the fine resolution of 10 × 10 m. We chose “Level-1C” (i.e., top-of-atmosphere reflectance) since it provides the longest data availability of Sentinel-2 images without any modification of the data. To build RGB images, we extracted the three bands B4, B3 and B2 that correspond to Red, Green and Blue channels, respectively. More bands available in Sentinel-2 or even in Sentinel-1 images can be incorporated in the future to our dataset. However, computational limitations (i.e., the size of the dataset would be impractical) did not allowed us to handle it as a first goal. In addition, the spatial resolution of the images would be heterogeneous across bands.To minimize the inherent noise due to atmospheric conditions (e.g. clouds, aerosols, smoke, etc.) that could affect the satellite RGB images, every image was built as a temporal aggregation of all images gathered by Sentinel-2 satellites between June 2015 and October 2020. During this aggregation, only the highest quality images in the corresponding image collection were considered, as we firstly discarded all image instances where the cloud probability exceeded 20% according to the metadata provided in their corresponding Sentinel-2 collection. Then, we calculated the 25th-percentile value between all remaining images for each reflectance band (R, G, and B), and built the final image with the obtained 25-percentile values in each pixel for its RGB bands. The 25th-percentile choice was adopted giving its suitability in atmospheric noise reduction44,45,46,47,48.Usually, Sentinel-2 MSI product includes true colour images in JPEG2000 format, except for the “Level-1C” collection used here. The three original bands (B4, B3, and B2) required a saturation mapping of their reflectance values into 0–255 RGB digital values. Thus, we mapped the saturation reflectance of 3558 into 255 to obtain true RGB channels with digital values between 0 and 255. The choice of these mapping numbers was taken from the Sentinel-2 true colour image recommendations section of Sentinel user guidelines. Finally, after exporting the selected tiles for each LULC class as “.tif” images, we converted them into “.jpeg” format using a lossless conversion algorithm.Technical implementationTo implement all our methodology steps, we first created a javascript in GEE for each LULC class. Each script is a multi-task javascript where we implemented a switch command to control which task we want to execute (between the spatio-temporal aggregation task, the spatial reprojection and tiles selection task, or the data exportation task). In each one of these scripts, we selected from GEE LULC datasets repository the 15 LULC products used to build the consensus of that LULC class. Each script was responsible of elaborating the spatio-temporal combination of the selected products and generating the final consensus map for that LULC class as described in the subsection “Combining products across time and space”. Then, it exports the final global probability map as an asset into GEE server storage to make its reprojection faster. In the same script, once the consensus map exportation was done, we imported it from the GEE assets storage and reprojected it to 2240 × 2240 m resolution; then, we exported the new reprojected map into GEE assets storage again to make its analysis and processing faster. Afterwards, we imported the reprojected map into the same script and applied different processing tasks. During this processing phase, many purity threshold values were evaluated. Then, we elaborated in this same script the pure tiles identification and their center coordinates exportation into a CSV file. A distinct GEE script was developed to import, reproject and export the global GHM map. The resulted GHM map was saved as an asset too, then imported and used in each one of the 29 LULC multi-task scripts.A python script was developed separately to read the exported CSV files for each LULC class and apply the reverse geo-referencing on their pure tiles coordinates then add the found geolocalization data (country code, locality…etc) to the original CSV files as new columns. Then, another python script was implemented to read the new resulted CSV files with all their added columns (reverse geo-referencing data, GHM data) and use the center coordinates of each pure tile in that class to export first its corresponding Sentinel-2 satellite geotiff image within GEE through the python API. Finally, after downloading all the selected geotiff images from our Google drive, we created another python script to convert these geotiff images into JPEG format. More

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DataSea Surface temperature (1850–2019)Sea Surface Temperature (SST, °C) from 1850 to 2019 originated from the COBE SST2 1° × 1° gridded dataset74, https://psl.noaa.gov/data/gridded/data.cobe2.html. SST data were interpolated on a 0.25° latitude × 0.25° longitude grid on a monthly scale from 1850 to 2019.BathymetryBathymetry (m) came from GEBCO Bathymetric Compilation Group 2019 (The GEBCO_2019 Grid—a continuous terrain model of the global oceans and land). Data are provided by the British Oceanographic Data Centre, National Oceanography Centre, NERC, UK. doi:10/c33m. (https://www.bodc.ac.uk/data/published_data_library/catalogue/10.5285/836f016a-33be-6ddc-e053-6c86abc0788e/). These data were interpolated on a 0.25° latitude × 0.25° longitude grid.Biological dataDaily mass concentration of chlorophyll-a in seawater (mg/m3) originated from the Glob Colour project (http://www.globcolour.info/). The product merges together all the daily data from satellites (MODIS, SeaWIFS, VIIRS) available from September 1997 to December 2019, on a 4 km resolution spatial grid. These data were interpolated on a daily scale on a 0.25° latitude × 0.25° longitude grid. These data were only used to map the average maximum standardised SSB (mdSSB) around the North Sea (Fig. 1a). When long-term changes in mdSSB were examined, we used modelled chlorophyll data (see section “Climate projections” below).Cod recrutment at age 1, Spawning Stock Biomass (SSB) and fishing effort F for 1963–2019 originated from ICES35.We used a plankton index of larval cod survival, which was an update of the index proposed by Beaugrand and colleagues33. Based on data from the Continuous Plankton Recorder (CPR)75, the index is based on the simultaneous consideration of six key biological parameters important for the diet and growth of cod larvae and juveniles in the North Sea:76,77 (i) Total calanoid copepod biomass as a quantitative indicator of food for larval cod, (ii) mean size of calanoid copepods as a qualitative indicator of food, (iii-iv) the abundance of the two dominant congeneric species Calanus finmarchicus and C. helgolandicus, (v) the genus Pseudocalanus and (vi) the taxonomic group euphausiids. A standardised Principal Component Analysis (PCA) is performed on the six plankton indicators for each month from March to September for the period 1958–2017 (table 60 years × 7 months-6 indicators). The plankton index is simply the first principal component of the PCA33.Climate projectionsClimate projections for SST and mass concentration of chlorophyll in seawater (kg m−3) originated from the Coupled Model Intercomparison Project Phase 6 (CMIP6)5 and were provided by the Earth System Grid Federation (ESGF). We used the projections known as Shared Socioeconomic Pathways (SSP) 245 and 585 corresponding respectively to a medium and a high radiative forcing by 2100 (2.5 W m−2 and 8.5 W m−2)78. The daily simulations of four different models (i.e. CNRM-ESM2-1, GFDL-ESM4, IPSL-CM6A-LR, and UKESM1-0-LL) covering the time period 1850–2014 (historical simulation) and 2015–2100 (future projections for the two SSPs scenarios) were used. All the data were interpolated on a 0.25° by 0.25° regular grid. Key references (i.e. DOI and dataset version) are provided in Supplementary Text 1. Long-term changes in modelled SSB were based on these data (including modelled daily chlorophyll data).The FishClim modelLet Kt be the maximum standardised Spawning Stock Biomass (mdSSB hereafter) that can be reached by a fish stock at time t for a given environmental regime φt. Xt+1, standardised SSB (dSSB hereafter) at time t+1 was calculated from dSSB at time t as follows:$${X}_{t+1}={X}_{t}+r{X}_{t}left(1-frac{{X}_{t}}{{K}_{t}}right)-alpha {X}_{t}$$
(1)
α is the fishing intensity that varies between 0 (i.e. no fishing) and 1 (i.e. 100% of SSB fished in a year). It is important to note that α (see Eq. (10)) should not be mistaken with ICES fishing effort F79 (calculated from SSB). The second term of Eq. (1) is the intrinsic growth rate of the fish stock that is a function of both Kt and the population growth rate r (r was fixed to 0.5 in most analyses, but see Fig. 3d however where r varied from 0.25 to 0.75). The population growth rate r is highly influenced by the life history traits of a species80 but also by environmental variability54,55,81. Here, the population growth rate was assumed to be constant in space and time and the influence of environmental variability occurred exclusively through its effects on Kt. We made this choice to not multiply the sources of complexity and errors (i.e. population growth rate is very difficult to assess and varies with age80). The third term reflects the part of dSSB that is lost by fishing. Note that natural mortality is not explicitly integrated in Eq. (1) because this process is difficult to assess with confidence at the scale of our study. Here, we assumed that the second term of Eq. (1) implicitly considered this process; when K increases, it is likely that natural mortality diminishes, especially at age 134. We tested this assumption below. Most of the time when fishing occurs, Xt {y}_{{{{rm{opt}}}}}$$
(3)
Here yopt= 5.4 °C and t1 and t2 were fixed to 5.7 °C and 4 °C, respectively, so that the thermal niche was close to that assessed by Beaugrand and colleagues31 (Supplementary Fig. 2). This Supplementary Figure compares the thermal response curve we chose in the present study with the data analysed in Beaugrand and colleagues31. The figure shows that the response curve (red curve) is close to the histogram showing the number of geographical cells with a cod occurrence as a function of temperature varying between −2 °C (frozen seawater) and 20 °C.Because t1  > t2, the niche was slightly negative asymmetrical (Supplementary Fig. 1). U1(y) was the first component of mdSSB along the thermal gradient y. c was the maximum value of mdSSB; c was fixed to 1 so that mdSSB varied between 0 and 184,85. y was the value of SST. Slight variations in the different parameters of the niche did not alter either the spatial patterns in the distribution of mdSSB nor the correlations with recruitment.To model the bathymetric niche of cod, we used a trapezoidal function. Changes in mdSSB, U2, along bathymetry, were assessed using four points (θ1, θ2, θ3, θ4):$$begin{array}{cc}{{U}}_2({{z}})=0 & {{{{{{{rm{When}}}}}}; z}}le {{{{rm{theta }}}}}_{1}end{array}$$
(4)
$$begin{array}{cc}{{U}}_2({{z}})=frac{z-{theta }_{1}}{{theta }_{2}-{theta }_{1}}c & {{{{{rm{When}}}}}},{{{{rm{theta }}}}}_{1} < {{z}}le {{{{rm{theta }}}}}_{2}end{array}$$ (5) $$begin{array}{cc}{{U}}_2({{z}})={{c}} & {{{rm{When}}}},{{{{rm{theta }}}}}_{2} < {{z}} < {{{{rm{theta }}}}}_{3}end{array}$$ (6) $${{U}}_2begin{array}{cc}(z)=frac{{theta }_{4}-z}{{theta }_{4}-{theta }_{3}}c & {{{rm{When}}}},{{{{rm{theta }}}}}_{3}le {{z}} < {{{{rm{theta }}}}}_{4}end{array}$$ (7) $$begin{array}{cc}{{{rm{U}}}}_2({{z}})=0 & {{{rm{When}}}}; {{{rm{z}}}}ge {{{theta }}}_{4}end{array}$$ (8) With θ2 ≥ θ1, θ3 ≥ θ2 and θ4≥ θ3 and y the bathymetry; θ1 = 0, θ2 = 10−4, θ3 = 200 and θ4 = 600 m (Supplementary Fig. 1). These parameters were retrieved from the litterature86,87. Here also c, the maximum abundance reached by the target species was fixed to 1 and U2 varied between 0 and 1. Trapezoidal niches have been used frequently to model the spatial distribution of fish and marine mammals88,89.The trophic niche was modelled by a rectangular function on a daily basis. To the best of our knowledge, no information on the trophic niche is available. We modelled the trophic niche by fixing U3 to 1 when chlorophyll-a concentration was higher than 0.05 mg m−3 during a minimum period of 15 days and 0 otherwise (Supplementary Fig. 1). This minimum of chlorophyll was implemented as a proxy for suitable food, which has been shown to be important in the North Atlantic for cod recruitment and distribution6,33.There exists two ways to combine the different ecological dimensions of a niche: (i) use an additive or (ii) a multiplicative model82,90. We used a multiplicative model because when one dimension is associated to a nil abundance, the resulting abundance combining all dimensions is also nil in contrast to an additive model; therefore only one unsuitable environmental value may explain a nil abundance. All dimensions were associated to abundance values that varied between 0 and 190.Therefore, maximum dSSB, K, for a given environmental regime E was given by multiplying the three niches (thermal, bathymetric and trophic):$$K=mathop{prod }limits_{i=1}^{p}{U}_{i}$$ (9) where p = 3, the three dimensions of the niche.AnalysesMapping of maximum standardised SSBmdSSB is close to the “dynamic B0” approach; B0 is the SSB in the absence of fishing (generally expressed in tonnes)51 whereas mdSSB is the SSB in the absence of fishing standardised between 0 and 1 and assessed from the knowledge of the niche of the species. We first assessed mdSSB in the North-east Atlantic (around UK) at a spatial resolution of 0.25° latitude × 0.25° longitude on a daily basis from 1850 to 2019. For this analysis, FishClim was run on monthly COBE SST (1850–2019), mean bathymetry and a climatology of daily mass concentration of chlorophyll-a in seawater from the Glob Colour project (see Data section). We then calculated an annual average based on the main seasonal productive period around UK, i.e. from March to October90. Finally, we averaged all years to examine spatial patterns in mean mdSSB (Fig. 1a).Temporal changes in maximum standardised SSBWe assessed average long-term changes in mdSSB in the North Sea (51°N–62°N and 3°W–9.5°E); the annual average was calculated from March to October because this is a period of high production90 . We compared long-term changes in mdSSB with cod recruitment at age 1, a plankton index of larval cod survival based on the period March to October33, and ICES-based SSB35 for 1963-2019 (Fig. 1b–d).Correlation analyses with modelled maximum standardised SSBPearson correlations between long-term changes in mdSSB (average for the North Sea, 51°N–62°N and 3°W–9.5°E) and cod recruitment at age 1 in decimal logarithm35, a plankton index of larval cod survival in the North Sea33, and observed ICES SSB in decimal logarithm35 for the period 1963–2019 were calculated (Fig. 1b–d). The same analysis was performed between assessed fishing intensity α from our FishClim model and fishing effort F35 in the North Sea (Fig. 1e). The probability of significance of the coefficients of correlation was adjusted to correct for temporal autocorrelation91.Assessment of fishing intensity from ICES spawning stock biomassUsing North Sea ICES SSB, we applied Eq. (1) to assess fishing intensity α:$$alpha =1+rleft(1-frac{{X}_{t}}{{K}_{t}}right)-frac{{X}_{t+1}}{{X}_{t}}$$ (10) With Xt+1 and Xt the ICES dSSB (in decimal logarithm). Standardisation of ICES SSB, necessary for this analysis, was complicated because many different kinds of standardisation were achievable so long as X remained strictly above 0 (i.e. full cod extirpation, not observed so far35) and strictly below min(K) (i.e. all black curves always below all points of the blue curve were possible, Supplementary Fig. 3). Indeed, ICES SSB includes exploitation and environmental fluctuations whereas K (i.e. mdSSB) integrates only environmental forcing; the difference is mainly caused by the negative influence of fishing. We chose the black curve (ICES SSB) that maximised the correlation between α (fishing intensity in the FishClim model) and F (ICES fishing effort)35.Reconstruction of long-term changes in ICES spawning stock biomassThe estimation of α allowed us to reconstruct long-term changes in cod (ICES) dSSB and to examine the respective influence of fishing and CIEC by means of Eq. (1) (“Methods”) using four hypothetical scenarios (Fig. 1f). First, we fixed fishing intensity and considered exclusively environmental variations through its influence on dSSB. (i–ii) We assessed long-term changes in dSSB from long-term variation in observed mdSSB (called Kt in Eq. (1)) with a constant level of exploitation fixed to (i) minimum (upper blue curve, i.e. the lowest fishing intensity observed in 1963–2019) or (ii) maximum (lower blue curve, i.e. the highest fishing intensity observed in 1963–2019).Second, we fixed the environmental influence on dSSB and considered variations in fishing intensity. We estimated long-term changes in dSSB from long-term variation in estimated α with a constant mdSSB fixed to (iii) minimum (lower red curve, i.e. the lowest mdSSB observed in 1963–2019) or (iv) maximum (upper red curve, i.e. the highest mdSSB observed in 1963–2019). It was possible to compare long-term changes in reconstructed (ICES) dSSB (thick black curve in Fig. 1f) with these four hypothetical scenarios (Fig. 1f); note that these comparisons were not affected by the choice we made earlier on the standardisation of (ICES) SSB.Quantification of the respective influence of fishing and climate/environment on spawning stock biomassUsing the previous curves, we examined the respective influence of fishing and CIEC on reconstructed (ICES) dSSB (Fig. 2). First, the influence of fishing was investigated by estimating the residuals between reconstructed (ICES) dSSB based on long-term changes in mdSSB (i.e. Kt in Eq. (1)) and α (thick black curves in Fig. 1f) and modelled dSSB based on fluctuating fishing intensity α and invariant K (average of the two red curves in Fig. 1f). This calculation led to the red curve in Fig. 2b. Next, we performed the opposite procedure to examine the influence of CIEC on dSSB (i.e. invariant fishing intensity α based on the two blue curves in Fig. 1f). This calculation led to the blue curve in Fig. 2b.A cluster analysis, based on a matrix years × three time series with (i) long-term changes in reconstructed standardised (ICES) SSBs, (ii) fishing and (iii) CIEC, was performed to identify key periods (vertical dashed lines in Fig. 2). We standardised each variable between 0 and 1 and used an Euclidean distance to assess the year (1963–2019) × year (1963–2019) square matrix so that each variable contributed equally to each association coefficient. We used an agglomerative hierarchical clustering technique using average linkage, which was a good compromise between the two extreme single and complete clustering techniques92. In this paper, we were only interested in the timing between the different time periods (i.e. the groups of years) revealed by the cluster analysis (Fig. 2).We also calculated an index of fishing influence (ε, expressed in percentage) by means of two indicators γ and δ, which were slightly different to the ones we used above. The first one, γ, was modelled dSSB with fluctuating fishing intensity and a constant mdSSB based on the best suitable environment observed during 1963–2019 (only the upper red curve in Fig. 1f; fishing influence). The second one, δ, was modelled dSSB based on fluctuating environment and fishing intensity (black curve in Fig. 1f) on modelled dSSB based on a fluctuating environment but a constant fishing intensity fixed to the lowest value of the time series (only the upper blue curve in Fig. 1f; environmental influence). The index of fishing influence (ε, expressed in percentage) was calculated as follows:$$varepsilon =frac{100gamma }{gamma +delta }$$ (11) For each period of 1963–2019 identified by the cluster analysis, we quantified the influence of fishing (and therefore the environment) using a Jackknife procedure93,94. The resampling procedure recalculated ε by removing each time 1 year of the time period, which allowed us to provide a range of values (i.e. minimum and maximum) in addition to the average value (bar{varepsilon }) calculated for each interval, including the whole period (Fig. 2c).Long-term changes in modelled spawning stock biomass (1850–2019, 2020–2100 and 2020-2300)We modelled mdSSB (Kt in Eq. (1)) using outputs from four Earth System models (ESMs) based on two scenarios of SST/Chlorophyll changes (i.e. SSP245 and SSP585) for the period 1850–2100 (and for one scenario and one ESM until 2300; Fig. 3).For the period 1850–2019, we used daily SST/Chlorophyll changes from the four ESMs to estimate potential changes in mdSSB (thin dashed black curves in Fig. 3a). An average of mdSSB was also calculated (thick green curve in Fig. 3a).For the period 2020–2100, we showed all potential changes in mdSSB based on the four ESMs and both scenarios SSP245 (thin dashed blue curves in Fig. 3a) and SSP585 (thin dashed red curves). An average of mdSSB was also calculated for scenarios SSP245 (thick continuous blue curve) and SSP585 (thick continuous red curve). In addition, we assessed dSSB based on a constant standardised catch fixed to the average of 2008–2019, the last period identified by the cluster analysis (G5, i.e. (alpha X) = 0.03 in Eq. (1)), and the average values of all ESMs for SSP245 (thick dashed blue curve in Fig. 3a) and SSP585 (thick dashed red curve). This analysis was performed to show how a constant catch might alter long-term changes in mdSSB. When Xt (Eq. (1)) reached 0.1, the stock was considered as fully extirpated.Understanding how fishing and climate/environment interact now and in the futureWe modelled dSSB as a function of fishing intensity α and CIEC to show how fishing and the environment interact (Fig. 3b, c). We calculated dSSB for fishing intensity between α = 0 and α = 0.5 every step Ɵ = 0.001 and for mdSSB between K = 0 and K = 1 every step Ɵ = 0.001 to represent values of dSSB as a function of fishing and CIEC. We then superimposed reconstructed ICES dSSB (1963–2019) on the diagram for three periods: 1963–1985 (high SSB), 1986–1999 (pronounced reduction in SSB), and 2000–2019 (low SSB). Maximum standardised SSB for 2020–2100 (or 2300 exclusively for Scenario SSP 585 of IPSL ESM) assessed from four ESMs and scenarios SSP245 and SSP585 were also superimposed. Fishing intensity is unpredictable for 2020–2100 and so we arbitrarily fixed it constant between 0.08 and 0.17 in increments of 0.1 for display purposes, starting by ESMs based on scenario SSP 245 followed by scenario SSP 585 (Fig. 3b). When Xt (Eq. (1)) reached 0.1, the stock was considered as fully extirpated.We calculated an index of sensitivity of dSSB as a function of fishing intensity and CIEC. To do so, we first calculated sensitivity of dSSB to fishing intensity α. Index ζi was calculated at point i from dSSB X and fishing intensity α at i−1 and i+1 (see also Eq. (1)):$$begin{array}{cc}{zeta }_{i}=frac{left|{X}_{i+1}-{X}_{i-1}right|}{left|{alpha }_{i+1}-{alpha }_{i-1}right|} & {{{rm{with}}}},{{{rm{min }}}}(alpha )+{{uptheta }}le ile {{{rm{max }}}}(alpha )-{{uptheta }}end{array}$$ (12) With min(α) = 0, max(α) = 0.5 and Ɵ = 0.001.Similarly, we calculated sensitivity of dSSB to K. Index ηj was calculated at point j from dSSB X and mdSSB K at j−1 and j+1 (see also Eq. (1)):$$begin{array}{cc}{eta }_{j}=frac{left|{X}_{j+1}-{X}_{j-1}right|}{left|{K}_{j+1}-{K}_{j-1}right|} & {{{rm{with}}}},{{{rm{min }}}}left(Kright)+{{{rm{theta }}}}le {{j}}le {{{rm{max }}}}({{{rm{K}}}})-{{uptheta }}end{array}$$ (13) With min(K) = 0, max(K) = 1 and Ɵ = 0.001.Then, we summed the two indices to assess the joint sensitivity of dSSB to fishing intensity Z and mdSSB H:$${{{{bf{I}}}}}_{{{i}},{{j}}}={{{bf{Z}}}}({{{{rm{zeta }}}}}_{{{i}}})+{{{bf{H}}}}({eta }_{{{j}}})$$ (14) Matrix I was subsequently standardised between 0 and 1:$${{{{boldsymbol{I}}}}}^{{{{boldsymbol{* }}}}}=frac{{{{boldsymbol{I}}}}-min ({{{boldsymbol{I}}}})}{max left({{{boldsymbol{I}}}}right)-min ({{{boldsymbol{I}}}})}$$ (15) With I* the matrix of sensitivity of dSSB to fishing intensity and mdSSB standardised between 0 and 1 (Fig. 3c).Number of years needed for recovery after stock collapseWe investigated how the number of years needed for a stock to recover after stock collapse (i.e. dSSB=0.05 in Eq. (1); i.e. 10% of mdSSB) varied as a function of mdSSB (between 0 and 1 by increment of 0.001); this was only influenced by the environmental regime φt and population growth rate r. For this analysis, we fixed a target dSSB of 0.4 (vertical dashed green vertical line in Fig. 3d) and three different values of r: 0.25, 0.5 and 0.75. We simulated a hypothetical moratorium with a fishing intensity α = 0 in Eq. (1).Here, stock collapse was defined as dSSB ≤ 0.1 × mdSSB, i.e. when the dSSB reached less than 10% of the unfished biomass mdSSB. This threshold corresponds to values usually defined in the literature; e.g. Pinsky and colleagues95 defined a collapse when landings are below 10% the average of the five highest landings recorded for more than 2 years, Worm and colleagues69 defined stock collapse when the biomass becomes lower than 10% of the unfished biomass, Andersen96 when it is lower than 20% and Thorpe and De Oliveira67 when it is lower than 10–20%.Potential consequences of fisheries management and climate-induced environmental changesWe examined how fishing and CIEC may affect cod stocks and their exploitation around UK with a focus in the North Sea (Figs. 4, 5). For these analyses, we averaged long-term changes in modelled dSSB corresponding to each scenario (all thin dashed blue and thin red curves in Fig. 3a for SSP245 and 585, respectively). In these analyses, the stock was considered fully extirpated when Xt (Eq. (1)) reached 0.1.Year of cod extirpation for 2020–2100 We estimated year of cod extirpation from 2020 to 2100 in each geographical cell based on (i) a constant fishing intensity (α = 0.04) in time and space, and (ii) an adjusted fishing intensity using the concept of Mean Sustainable Yield (MSY). The choice of α = 0.04 did not alter our conclusions; a lower or a higher value delayed or speed cod extirpation in a predictable way, respectively. In fisheries, MSY is defined as the maximum catch (abundance or biomass) that can be removed from a population over an indefinite period with dX/dt = 0, with X for dSSB and t for time. Despite some criticisms about MSY66, the concept remains a key paradigm in fisheries management35,63. We used this concept to show that controlling fishing intensity delayed cod extirpation. From Eq. (1), we calculated fishing intensity, called αMSYt, so that X remained above XMSYt at all time t:$${alpha }_{{{{{rm{MSY}}}}t}}=rleft(1-frac{{X}_{{{{{rm{MSY}}}}t}}}{{K}_{t}}right)$$ (16) In this analysis, we fixed XMSY t = Kt/2. We assessed ({alpha }_{{{{{rm{MSY}}}}t}}) from Eq. (16) and then estimated dSSB from ({alpha }_{{{{{rm{MSY}}}}t}}) and Kt (based on averaged SSP245 and SSP585) by means of Eq. (1). Although results were displayed at the scale of the north-east Atlantic (around UK), we calculated the difference in year of cod extirpation between scenarios of warming (SSP245 and SSP585) and between scenarios of cod management (constant versus adjusted—MSY— fishing intensity). Differences were presented by means of histograms (Fig. 4). From each histogram, we calculated the median of the differences in year of cod extirpation E97. Pooled standardised catch by 2100 (2020–2100) In term of fishing exploitation, we assessed pooled standardised catch (i.e. pooled dSSB) in 2100 (2020–2100), again for two scenarios of CIEC (SSP245 and 585) and two scenarios of cod management (constant versus adjusted—MSY—fishing intensity; Fig. 5). We then calculated the percentage of reduction in pooled standardised catch caused by fishing or the intensity of warming. Finally, we assessed the median of the percentage of reduction in pooled standardised catch for the North Sea area (51°N–62°N and 3°W–9.5°E). The goal of this analysis was to demonstrate that controlling fishing intensity optimises cod exploitation. Statistics and reproducibilityAll statistical analyses can be reproduced from the equations provided in the text, the cited references or the data available in Supplementary Data.Reporting summaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More

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