Extended Data Fig. 7: GAM-model diagnostics of ambient temperatures during spawning migration.

Temperature data were analysed from three monitoring stations (Bud, Eggum and Ingøy) located at different latitudes along the Norwegian shelf (Extended Data Fig. 5a). Data were collected over a 30-year period (1995–2024) from 15 January through March at depths 50–200 m, representing water masses experienced by adult herring on spawning migration and their incubated eggs until peak hatching. A GAM model was fitted separately to data from each of the three monitoring stations: Temp ~ s(Year, k = 17) + s(DayOfYear, k = 5) + s(Depth, k = 5). All three models, Bud (n = 642, R² = 0.743, p < 0.001), Eggum (n = 1162, R² = 0.720, p < 0.001) and Ingøy (N = 1032, R² = 0.589, p < 0.001) as well as their intercepts and smoothers (DayOfYear, Depth, Year, p < 0.001) were highly significant. Output: a, Distribution of raw data over day of year for the three models. b, c, d Partial effects of smoother terms at their covariate means (values inside each panel, DayOfYear = Doy) with 95% CIs. e, f, Model diagnostic plots showing e, fitted values versus residuals and f, QQ plots.