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The African Development Corridors database is publicly available. The visualisation of the database that can be explored interactively here: https://dcp-unep-wcmc.opendata.arcgis.com/. The data is deposited in the Dryad Digital Repository referenced as Thorn, J. P.R., Mwangi, B.; Juffe Bignoli, D., The African Development Corridors Database, Dryad, Dataset, https://doi.org/10.5061/dryad.9kd51c5hw (2022)43. The final data were compiled into an online Master database spreadsheet, using the project code data as the merging attribute of the spatial and tabular database (AfricanDevelopmentCorridorsDatabase2022.csv). The African Development Corridor Database is presented as a GeoPackage file (.gpkg) and ESRI file Geodatabase (.gdb) composed by line and point feature datasets with the 22 associated attributes for all mapped corridors, a table with corridors that could not be mapped (also with the attributes), and a table with all sources consulted for each project code.We created a data standard to ensure a systematic and standardised data collection (Supplementary Table 2). Each data record in the database represents a project within a development corridor. To group all projects within the same development corridor we used a unique identifier composed by three letters that identified the corridor plus a number unique for each project or record. For example, the Lamu port project in Kenya within the Lamu Port South Sudan Ethiopia Transport Corridor (LAPSSET) was represented as LAP000. In this corridor we identified 20 projects, from LAP0001 which is the Lamu Port to LAP0020 which is the Isiolo-Lokichar-Lodwar-Nadapal Highway in Kenya. In addition to the unique identifier for each project, the data standard includes data attributes that provide detailed information about each project. Table 1 describes the attributes included in the database. Supplementary Table 3 summarises the 79 corridors included in the database.Table 1 List of the attributes included in the African Development Corridors Database.Full size tableInfrastructure types and status of development corridors in AfricaThe data consists of a total of 79 corridors consisting of 184 projects (Fig. 2). Of the 12 infrastructure types, the most predominant form of infrastructure in Africa’s development corridors is roads (n = 64, 34.8%), followed by wet ports (n = 38, 20.7%), passenger and freight railways (n = 33, 17.9%), and airports (n = 14, 7.6%). Fewer resort cities, electricity transmission lines, dry ports, industrial parks, and water pipelines comprise development corridors (all ≤ n = 3, 1.6%) (Fig. 3). We acknowledge our study might not include many infrastructure developments that are components projects of larger programmes but are not yet labelled as corridors. A total of 107 (58.7%) projects are operational, 35 (19%) are in progress, 25 (13.6%) are planned, 25 (13.9%) are being upgraded, and 2(1%) are on hold.Fig. 2Map showing the distribution of all the development corridors included in the African Development Corridors Database and their infrastructure type.Full size imageFig. 3Subset of highest frequencies of key attributes captured in the database.Full size imageSpatial distributionThe linear distance of development corridors in Africa is 122,294 km – which approximates to three times the Earth’s circumference, with an average of 1703.84 ± 213.19 km (mean, SE), ranging from 4–11,141 km. In terms of number of projects per country, Kenya has the most projects (n = 34, 18.5%), followed by Tanzania (n = 18, 9.8%), South Africa and Democratic Republic of the Congo (n = 17, 9.2% ea.), Ethiopia (n = 15, 8.2%), Mozambique and Zambia (n = 14, 7.6%), Angola, Uganda, Guinea and Cameroon (n = 12, 6.5%), Namibia (n = 11, 6.0%), Republic of Congo (n = 10, 5.4%), Burundi and Chad (n = 9, 4.9%), Malawi, Senegal, and Zimbabwe (n = 8, 4.4%), and Burkina Faso and Ghana (n = 7, 3.8%). Due to differences in the frequency and quality that countries publish data on infrastructure and development corridor investments, coverage may be lower for some regions, or some periods (i.e., recent, or further in the past).Investments in development corridorsAdjusting for inflation, the total investment of development corridors that is captured in the database ranges between USD 547.29–658.62 billion. The average cost of a corridor ranges between USD 3.46 ± 1.92 billion and USD 4.17 ± 2.04 billion. This is a notable sum, considering the average GDP in sub-Saharan Africa is USD 1.48 billion44. The most expensive development corridor project is the first of the nine Trans African Highway projects at USD 78.20 billion (when adjusted for inflation) – comprising transcontinental roads across Africa. We were able to capture the budget (or at least a proportion of the budget) for 84.7% of all projects.Temporal evolution of growth of development corridorsInvestments started in the 1800s and have increased exponentially (Fig. 4). Over a fifty-year period, the greatest number of investments took place between 1950 and 2000. Spikes in investments occurred particularly around 1900, which was when there was a wave of new imperialism across the continent, followed in the 1960s when many countries across sub-Saharan Africa gained independence. The third spike in investment was in the last decade, particularly since 2013, when we have seen rapid growth in foreign direct investment in Africa under initiatives such as the Belt and Road Initiative. According to the Ernst and Young Africa Attractiveness Survey (2019)45, the largest foreign direct investment (in terms of capital) between 2014–2018 came from China (USD 72,235 million), France (USD 34,172 million), USA (USD 30,885 million), the United Arab Emirates (USD 25,278 million) and the United Kingdom (USD 17,768 million).Fig. 4(a) Temporal evolution of investment in development corridors in Africa. (b) Annual investments per annum in development corridors in Africa (USD maximum, before adjusting for inflation).Full size imageDonors that are funding development corridorsAcross Africa, regional development banks invested the most in development corridors (30.8%), with the African Development Bank funding the majority (24.3%) of all projects. Outside of Africa, the regional development banks that invested in the most projects are the Export-Import Bank of China (n = 13, 3.8%), the European Investment Bank (n = 10, 2.8%) and the Arab Bank for Economic Development in Africa (n = 4, 1.2% ea.). National governments funded about 29.8% of all projects. The Government of Kenya funded the most projects (n = 26; 7.5%), followed by the Governments of Tanzania (n = 7, 2.0%) and South Africa (n = 4, 1.2%). Multilateral banks funded 10.9% of projects – mostly from the World Bank (n = 33, 9.54%) and a few from the International Finance Corporation (n = 4, 1.6%). The international development community funded only 6.1% – of which the OPEC Fund for International Development funded four projects. Private companies continue to invest in a small percentage of development corridors (3.5%), but this is higher than national banks that invest in 3.2%. Regional Economic Community bodies have invested in 15 (4.8%) of all 184 projects. The average number of donors per corridor ranged from one to 12.Weighting of investments by donor typeIn terms capital funded per donor type, Regional Development Banks invested the most (totalling USD 30.72 billion), followed by national governments (USD 20.45 billion). The figure then drops substantially to international development agencies (USD6.17 billion) and multilateral banks (USD 3.76 billion). These results are limited by the fact that we were only able to capture the amount funded delineated by donor type for 22.58% (or USD 70.24 billion) of the minimum of all investments (USD 311.14 billion) before adjusting for inflation.Commodities transportedA total of 147 commodities were captured. The top twenty commodities traded were rice (n = 52, 28.7% of all projects), sugar (27.0%), fish and petroleum (24.3% ea.), passengers (21.6%), textiles (21.1%), maize (19.5%), coffee (18.9%), cement and timber (17.8% ea.) followed by cotton, crude petroleum, vehicle spare parts, beverages, copper, fruit, fertilisers, gold, pharmaceutical products, and tobacco.Beneficiaries and net supplier or receiverApproximately 213 different beneficiaries were identified – predominantly local communities (n = 134 of projects, 72.8%), followed by national and local governments (63.0%), traders (51.1%), agricultural farmers and livestock producers (27.7%), ports (27.2%), industries (25.5%), truck drivers (22.3%), tourists (17.4%), entrepreneurs (12.0%), and logistics companies (11.4%). Almost all (89.1%) of corridors are net receivers and suppliers of commodities, while only 13 (7.1%) are net suppliers and seven are net receivers (3.8%). 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