Supplementary Material

Figure S1. Visualisation of the spatial structure used to approximate the spatial variation in each case-study (after projecting Latitude/Longitude to UTM coordinates measured in eastings (x-axis) and northings (y-axis). Red circles show the location of interior knots (50 for the local zone and 150 for the global zone) where this dots was chosen a priori and knots were then allocated using a k-means algorithm in proportion to the available sampling data. Black dots represent the extrapolation-grid (≃ 0.227° for local zone and ≃ 0.45° for the global zone) used when approximating the integral across the fishing location.

Figure S2. Abundance indices (A; representing total biomass at the chosen spatial domain, in metric tons), effective area occupied (B; representing area needed to contain the population at average biomass-density, in km2), and northward (C) - eastward (D) center-of-gravity (C and D; representing the centroid of the population) each showing bias-corrected maximum likelihood estimate (ovals) and +/- one standard error (whisker) for each quarterly index of the adult yellowfin tuna resource in the global area; the period is from 1993 to 2018 (26 years * 4 =104 quarters).

Figure S3. Abundance indices (A; representing total biomass at the chosen spatial domain, in metric tonnes), effective area occupied (B; representing area needed to contain the population at average biomass-density, in km2), and northward (C) - eastward (D) center-of-gravity (C and D; representing centroid of the population) each showing bias-corrected maximum likelihood estimate (ovals) and +/- one standard error (whisker) for each quarterly index of the adult yellowfin tuna resource in the EEZ of Côte d’Ivoire; the period is from 1993 to 2018 (26 years *4 =104 quarters).

Figure S4. The predicted geometric anisotropy for the GLOBAL model. The ellipses give the 10% decorrelation distance for each of the two model components (delta model).

Figure S5. The predicted geometric anisotropy for the LOCAL model. The ellipses give the 10% decorrelation distance for each of the two model components (delta model).

Figure S6. A)The quantile-quantile plot of residuals (left) and plot of how residuals vary with magnitude of the prediction (right). B) Spatial map of quantile residuals by quarter. Results for the GLOBAL area.

Figure S7. A)The quantile-quantile plot of residuals (left) and plot of how residuals vary with the magnitude of the prediction (right). B) Spatial map of quantile residuals per quarter. Results for the LOCAL area.

Figure S8. Geographical distribution of yellowfin tuna total catches by major gears in the Atlantic Ocean (ICCAT zone) from 2010 to 2016 (Source: ICCAT, 2019).

Figure S9. Overview of a hypothetical spawning migration pattern of adult yellowfin, from the North Central Atlantic Ocean in summer, to the Gulf of Guinea before, during and after each 1st quarter (from Fonteneau et al., 2017).

Figure S10. ICCAT recommendations since their introduction in 1999. FAD stands for fish aggregating devices. (figure from (Stephan et al. 2022)).

Table S1 Summary details of the models used in this application. For each model, the following information is given: number of fixed effects, number of random effects, total estimated parameters and maximum gradient component.

Table S2 Abundance indices per year-quarter

© S. A. V. Akia et al., Published by EDP Sciences 2023